Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems

T. J. Vongkovit, Hansveer Singh, Romain Vasseur, Sarang Gopalakrishnan


The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak quasiperiodic modulations; however, as the quasiperiodic modulation gets increasingly strong, it is increasingly renormalized and eventually fails, as the system becomes ... [click to read more]

localized. We explore how quasiperiodic modulation renormalizes the Luttinger parameter characterizing this emergent Luttinger liquid, using the renormalization of transmission coefficients across a barrier as a proxy that remains valid for general quasiperiodic modulation. We find, unexpectedly, that quasiperiodic modulation weakens the effects of short-range interactions, but enhances those of long-range interactions. We support the former finding with matrix-product numerics. We also discuss how interactions affect the localization phase boundary.

Slow crossover from superdiffusion to diffusion in isotropic spin chains

Catherine McCarthy, Sarang Gopalakrishnan, Romain Vasseur


Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous nonabelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet ... [click to read more]

isotropic perturbations of strength $\lambda$. We identify an anomalously-long crossover time scale $t_\star \sim \lambda^{-\alpha}$ with $\alpha \approx 6$ in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.

Trapped ion qubit and clock operations with a visible wavelength photonic coil resonator stabilized integrated Brillouin laser

Nitesh Chauhan, Christopher Caron, Jiawei Wang, Andrei Isichenko, Nishat Helaly, Kaikai Liu, Robert J. Niffenegger, Daniel J. Blumenthal


Integrating precise, stable, ultra-low noise visible light lasers into atomic systems is critical for advancing quantum information sciences and improving scalability and portability. Trapped ions are a leading approach for high-fidelity quantum computing, high-accuracy optical clocks, and precision quantum sensors. However, current ion-based systems rely on bulky, lab-scale precision lasers ... [click to read more]

and optical stabilization cavities for optical clock and qubit operations, constraining the size, weight, scalability, and portability of atomic systems. Chip-scale integration of ultra-low noise lasers and reference cavities operating directly at optical clock transitions and capable of qubit and clock operations will represent a major transformation in atom and trapped ion-based quantum technologies. However, this goal has remained elusive. Here we report the first demonstration of chip-scale optical clock and qubit operations on a trapped ion using a photonic integrated direct-drive visible wavelength Brillouin laser stabilized to an integrated 3-meter coil-resonator reference cavity and the optical clock transition of a $^{88}$Sr$^+$ ion trapped on a surface electrode chip. We also demonstrate for the first time, to the best of our knowledge, trapped-ion spectroscopy and qubit operations such as Rabi oscillations and high fidelity (99%) qubit state preparation and measurement (SPAM) using direct drive integrated photonic technologies without bulk optic stabilization cavities or second harmonic generation. Our chip-scale stabilized Brillouin laser exhibits a 6 kHz linewidth with the 0.4 Hz quadrupole transition of $^{88}$Sr$^+$ and a self-consistent coherence time of 60 $\mu$s via Ramsey interferometry on the trapped ion qubit. Furthermore, we demonstrate the stability of the locked Brillouin laser to 5$\times10^{-13}/ \sqrt{\tau}$ at 1 second using dual optical clocks.

Non-Gaussian diffusive fluctuations in Dirac fluids

Sarang Gopalakrishnan, Ewan McCulloch, Romain Vasseur


Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in ... [click to read more]

conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals.

Universal structure of measurement-induced information in many-body ground states

Zihan Cheng, Rui Wen, Sarang Gopalakrishnan, Romain Vasseur, Andrew C. Potter


Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based ... [click to read more]

quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials.

Co-Designed Superconducting Architecture for Lattice Surgery of Surface Codes with Quantum Interface Routing Card

Charles Guinn, Samuel Stein, Esin Tureci, Guus Avis, Chenxu Liu, Stefan Krastanov, Andrew A. Houck, Ang Li


Facilitating the ability to achieve logical qubit error rates below physical qubit error rates, error correction is anticipated to play an important role in scaling quantum computers. While many algorithms require millions of physical qubits to be executed with error correction, current superconducting qubit systems contain only hundreds of physical ... [click to read more]

qubits. One of the most promising codes on the superconducting qubit platform is the surface code, requiring a realistically attainable error threshold and the ability to perform universal fault-tolerant quantum computing with local operations via lattice surgery and magic state injection. Surface code architectures easily generalize to single-chip planar layouts, however space and control hardware constraints point to limits on the number of qubits that can fit on one chip. Additionally, the planar routing on single-chip architectures leads to serialization of commuting gates and strain on classical decoding caused by large ancilla patches. A distributed multi-chip architecture utilizing the surface code can potentially solve these problems if one can optimize inter-chip gates, manage collisions in networking between chips, and minimize routing hardware costs. We propose QuIRC, a superconducting Quantum Interface Routing Card for Lattice Surgery between surface code modules inside of a single dilution refrigerator. QuIRC improves scaling by allowing connection of many modules, increases ancilla connectivity of surface code lattices, and offers improved transpilation of Pauli-based surface code circuits. QuIRC employs in-situ Entangled Pair (EP) generation protocols for communication. We explore potential topological layouts of QuIRC based on superconducting hardware fabrication constraints, and demonstrate reductions in ancilla patch size by up to 77.8%, and in layer transpilation size by 51.9% when compared to the single-chip case.

Generalized hydrodynamics: a perspective

Benjamin Doyon, Sarang Gopalakrishnan, Frederik Møller, Jörg Schmiedmayer, Romain Vasseur


Conventional hydrodynamics describes systems with few long-lived excitations. In one dimension, however, many experimentally relevant systems feature a large number of long-lived excitations even at high temperature, because they are proximate to integrable limits. Such models cannot be treated using conventional hydrodynamics. The framework of generalized hydrodynamics (GHD) was recently ... [click to read more]

developed to treat the dynamics of one-dimensional models: it combines ideas from integrability, hydrodynamics, and kinetic theory to come up with a quantitative theory of transport. GHD has successfully settled several longstanding questions about one-dimensional transport; it has also been leveraged to study dynamical questions beyond the transport of conserved quantities, and to systems that are not integrable. In this article we introduce the main ideas and predictions of GHD, survey some of the most recent theoretical extensions and experimental tests of the GHD framework, and discuss some open questions in transport that the GHD perspective might elucidate.

Observing quantum measurement collapse as a learnability phase transition

Utkarsh Agrawal, Javier Lopez-Piqueres, Romain Vasseur, Sarang Gopalakrishnan, Andrew C. Potter


The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining ... [click to read more]

coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware.

Extended critical phase in quasiperiodic quantum Hall systems

Jonas F Karcher, Romain Vasseur, Sarang Gopalakrishnan

Phys. Rev. B 109, 064208 - Published 26 February 2024

We consider the effects of quasiperiodic spatial modulation on the quantum Hall plateau transition, by analyzing the Chalker-Coddington network model for the integer quantum Hall transition with quasiperiodically modulated link phases. In the conventional case (uncorrelated random phases), there is a critical point separating topologically distinct integer quantum Hall insulators. ... [click to read more]

Surprisingly, the quasiperiodic version of the model supports an extended critical phase for some angles of modulation. We characterize this critical phase and the transitions between critical and insulating phases. For quasiperiodic potentials with two incommensurate wavelengths, the transitions we find are in a different universality class from the random transition. Upon adding more wavelengths they undergo a crossover to the uncorrelated random case. We expect our results to be relevant to the quantum Hall phases of twisted bilayer graphene or other Moir\'e systems with large unit cells.

Boundary transfer matrix spectrum of measurement-induced transitions

Abhishek Kumar, Kemal Aziz, Ahana Chakraborty, Andreas W. W. Ludwig, Sarang Gopalakrishnan, J. H. Pixley, Romain Vasseur

Phys. Rev. B 109, 014303 (2024)

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the ... [click to read more]

boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs.

Measurement induced criticality in quasiperiodic modulated random hybrid circuits

Gal Shkolnik, Aidan Zabalo, Romain Vasseur, David A. Huse, J. H. Pixley, Snir Gazit

Phys. Rev. B 108, 184204 (2023)

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\beta$ to exceed the Luck bound $\nu \ge 1/(1-\beta)$ for the stability of the MIPT where $\nu\cong ... [click to read more]

4/3$. Via large-scale numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $\beta$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\psi \cong \beta$, finding excellent agreement with the conclusions of real space renormalization group calculations.

Random insights into the complexity of two-dimensional tensor network calculations

Sofia Gonzalez-Garcia, Shengqi Sang, Timothy H. Hsieh, Sergio Boixo, Guifre Vidal, Andrew C. Potter, Romain Vasseur


Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically ... [click to read more]

a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states

Faster-than-Clifford Simulations of Entanglement Purification Circuits and Their Full-stack Optimization

Vaishnavi L. Addala, Shu Ge, Stefan Krastanov


Quantum Entanglement is a fundamentally important resource in Quantum Information Science; however, generating it in practice is plagued by noise and decoherence, limiting its utility. Entanglement distillation and forward error correction are the tools we employ to combat this noise, but designing the best distillation and error correction circuits that ... [click to read more]

function well, especially on today's imperfect hardware, is still challenging. Here, we develop a simulation algorithm for distillation circuits with gate-simulation complexity of $\mathcal{O}(1)$ steps, providing for drastically faster modeling compared to $\mathcal{O}(n)$ Clifford simulators or $\mathcal{O}(2^n)$ wavefunction simulators over $n$ qubits. This new simulator made it possible to not only model but also optimize practically interesting purification circuits. It enabled us to use a simple discrete optimization algorithm to design purification circuits from $n$ raw Bell pairs to $k$ purified pairs and study the use of these circuits in the teleportation of logical qubits in second-generation quantum repeaters. The resulting purification circuits are the best-known purification circuits for finite-size noisy hardware and can be fine-tuned for specific hardware error models. Furthermore, we design purification circuits that shape the correlations of errors in the purified pairs such that the performance of the error-correcting code used in teleportation or other higher-level protocols is greatly improved. Our approach of optimizing multiple layers of the networking stack, both the low-level entanglement purification, and the forward error correction on top of it, are shown to be indispensable for the design of high-performance second-generation quantum repeaters.

Quantum theory of single-photon nonlinearities generated by ensembles of emitters

Kurt Jacobs, Stefan Krastanov, Mikkel Heuck, Dirk R. Englund


The achievement of sufficiently fast interactions between two optical fields at the few-photon level would provide a key enabler for a broad range of quantum technologies. One critical hurdle in this endeavor is the lack of a comprehensive quantum theory of the generation of nonlinearities by ensembles of emitters. Distinct ... [click to read more]

approaches applicable to different regimes have yielded important insights: i) a semiclassical approach reveals that, for many-photon coherent fields, the contributions of independent emitters add independently allowing ensembles to produce strong optical nonlinearities via EIT; ii) a quantum analysis has shown that in the few-photon regime collective coupling effects prevent ensembles from inducing these strong nonlinearities. Rather surprisingly, experimental results with around twenty photons are in line with the semi-classical predictions. Theoretical analysis has been fragmented due to the difficulty of treating nonlinear many-body quantum systems. Here we are able to solve this problem by constructing a powerful theory of the generation of optical nonlinearities by single emitters and ensembles. The key to this construction is the application of perturbation theory to perturbations generated by subsystems. This theory reveals critical properties of ensembles that have long been obscure. The most remarkable of these is the discovery that quantum effects prevent ensembles generating single-photon nonlinearities only within the rotating-wave regime; outside this regime single-photon nonlinearities scale as the number of emitters. The theory we present here also provides an efficient way to calculate nonlinearities for arbitrary multi-level driving schemes, and we expect that it will prove a powerful foundation for further advances in this area.

Emergence of fluctuating hydrodynamics in chaotic quantum systems

Julian F. Wienand, Simon Karch, Alexander Impertro, Christian Schweizer, Ewan McCulloch, Romain Vasseur, Sarang Gopalakrishnan, Monika Aidelsburger, Immanuel Bloch


A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model ... [click to read more]

the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in hard-core boson ladders, contrasting systems with ballistic and chaotic dynamics. We find excellent agreement between our results and MFT predictions, which allows us to accurately extract diffusion constants from fluctuation growth. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, expanding the applicability of MFT to the quantum regime.

Resource-efficient fault-tolerant one-way quantum repeater with code concatenation

Kah Jen Wo, Guus Avis, Filip Rozpędek, Maria Flors Mor-Ruiz, Gregor Pieplow, Tim Schröder, Liang Jiang, Anders Søndberg Sørensen, Johannes Borregaard

npj Quantum Inf 9, 123 (2023)

One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum ... [click to read more]

error correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimal resource overhead by interspersing repeater nodes that each specializes in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

Tunable superdiffusion in integrable spin chains using correlated initial states

Hansveer Singh, Michael H. Kolodrubetz, Sarang Gopalakrishnan, Romain Vasseur


Although integrable spin chains only host ballistically propagating particles they can still feature diffusive spin transport. This diffusive spin transport originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long range correlations lead to superdiffusive spin transport with ... [click to read more]

a tunable dynamical exponent. We substantiate our prediction with numerical simulations and explain how deviations arise from finite time and finite size effects.

Superdiffusion from nonabelian symmetries in nearly integrable systems

Sarang Gopalakrishnan, Romain Vasseur

Annual Review of Condensed Matter Physics Vol. 15:159-176 (2024)

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads in time $t$ to a width $t^{2/3}$. This exponent, as well as the functional form of the dynamical ... [click to read more]

spin correlation function, suggest that spin transport is in the Kardar-Parisi-Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry, and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

Quantum turnstiles for robust measurement of full counting statistics

Rhine Samajdar, Ewan McCulloch, Vedika Khemani, Romain Vasseur, Sarang Gopalakrishnan


We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures ... [click to read more]

FCS starting from number-indefinite initial states or in the presence of noisy dynamics. In addition, by mapping the FCS onto a single-body observable, it allows for stable numerical calculations of FCS using approximate tensor-network methods. We demonstrate the wide-ranging utility of this approach by computing the FCS of the transferred magnetization in a Floquet Heisenberg spin chain, as studied in a recent experiment with superconducting qubits, as well as the FCS of charge transfer in random circuits.

Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits

Shayan Majidy, Utkarsh Agrawal, Sarang Gopalakrishnan, Andrew C. Potter, Romain Vasseur, Nicole Yunger Halpern

Phys. Rev. B 108, 054307 (2023)

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian ... [click to read more]

nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.

All-photonic GKP-qubit repeater using analog-information-assisted multiplexed entanglement ranking

Filip Rozpędek, Kaushik P. Seshadreesan, Paul Polakos, Liang Jiang, Saikat Guha

Phys. Rev. Research 5, 043056 (2023)

Long distance quantum communication will require the use of quantum repeaters to overcome the exponential attenuation of signal with distance. One class of such repeaters utilizes quantum error correction to overcome losses in the communication channel. Here we propose a novel strategy of using the bosonic Gottesman-Kitaev-Preskill (GKP) code in ... [click to read more]

a two-way repeater architecture with multiplexing. The crucial feature of the GKP code that we make use of is the fact that GKP qubits easily admit deterministic two-qubit gates, hence allowing for multiplexing without the need for generating large cluster states as required in previous all-photonic architectures based on discrete-variable codes. Moreover, alleviating the need for such clique-clusters entails that we are no longer limited to extraction of at most one end-to-end entangled pair from a single protocol run. In fact, thanks to the availability of the analog information generated during the measurements of the GKP qubits, we can design better entanglement swapping procedures in which we connect links based on their estimated quality. This enables us to use all the multiplexed links so that large number of links from a single protocol run can contribute to the generation of the end-to-end entanglement. We find that our architecture allows for high-rate end-to-end entanglement generation and is resilient to imperfections arising from finite squeezing in the GKP state preparation and homodyne detection inefficiency. In particular we show that long-distance quantum communication over more than 1000 km is possible even with less than 13 dB of GKP squeezing. We also quantify the number of GKP qubits needed for the implementation of our scheme and find that for good hardware parameters our scheme requires around $10^3-10^4$ GKP qubits per repeater per protocol run.

Near-term $n$ to $k$ distillation protocols using graph codes

Kenneth Goodenough, Sébastian de Bone, Vaishnavi L. Addala, Stefan Krastanov, Sarah Jansen, Dion Gijswijt, David Elkouss


Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distill $n$ to $k$ end-to-end entangled pairs using ... [click to read more]

bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.

Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems

Ewan McCulloch, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 131, 210402 (2023)

We investigate the full counting statistics of charge transport in $U(1)$-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system, and study the fluctuations of the charge transferred across the central bond in typical circuits. ... [click to read more]

Using an effective replica statistical mechanics model and a mapping onto an emergent classical stochastic process valid at large onsite Hilbert space dimension, we show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading $t^{-1/2}$ quantum corrections. We discuss our results in the context of fluctuating hydrodynamics and macroscopic fluctuation theory of classical non-equilibrium systems, and check our predictions against direct matrix-product state calculations.

Triviality of quantum trajectories close to a directed percolation transition

Lorenzo Piroli, Yaodong Li, Romain Vasseur, Adam Nahum

Phys. Rev. B 107, 224303 (2023)

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state ... [click to read more]

(taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback.

Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains

Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 131, 197102 (2023)

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ/stochastic Burgers equation, which force higher-order spin ... [click to read more]

fluctuations to deviate from standard KPZ predictions. We put forward a non-linear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.

Integrability breaking from backscattering

Javier Lopez-Piqueres, Romain Vasseur

Phys. Rev. Lett. 130, 247101 (2023)

We analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability and leads to a crossover from ballistic to diffusive transport, it preserves infinitely many conserved quantities corresponding to even moments of the velocity distribution of the gas. In the ... [click to read more]

limit of small noise, we derive the exact expressions for the diffusion and structure factor matrices, and show that they generically have off-diagonal components in the presence of interactions. We find that the particle density structure factor is non-Gaussian and singular near the origin, with a return probability showing logarithmic deviations from diffusion.

Hydrodynamic relaxation of spin helices

Guillaume Cecile, Sarang Gopalakrishnan, Romain Vasseur, Jacopo De Nardis

Phys. Rev. B 108, 075135 (2023)

Motivated by recent cold atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of helices, combining generalized hydrodynamics (GHD) with diffusive ... [click to read more]

corrections and the local density approximation. Although helices are far from local equilibrium (so GHD need not apply a priori), our theory reproduces the experimentally observed relaxational dynamics of helices. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes.

Anomalous transport from hot quasiparticles in interacting spin chains

Sarang Gopalakrishnan, Romain Vasseur

Rep. Prog. Phys. 86 036502 (2023)

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, high-temperature spin transport can be diffusive or superdiffusive. We review the transport properties of this ... [click to read more]

model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

Transitions in the learnability of global charges from local measurements

Fergus Barratt, Utkarsh Agrawal, Andrew C. Potter, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 129, 200602 (2022)

We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the ... [click to read more]

eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.

Infinite-randomness criticality in monitored quantum dynamics with static disorder

Aidan Zabalo, Justin H. Wilson, Michael J. Gullans, Romain Vasseur, Sarang Gopalakrishnan, David A. Huse, J. H. Pixley

Phys. Rev. B 107, L220204 (2023)

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In ... [click to read more]

particular, at the critical measurement rate, we find that the entanglement of a subsystem of size $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, the dynamical critical exponent $z = \infty$. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.

All-Photonic Artificial Neural Network Processor Via Non-linear Optics

Jasvith Raj Basani, Mikkel Heuck, Dirk R. Englund, Stefan Krastanov


Optics and photonics has recently captured interest as a platform to accelerate linear matrix processing, that has been deemed as a bottleneck in traditional digital electronic architectures. In this paper, we propose an all-photonic artificial neural network processor wherein information is encoded in the amplitudes of frequency modes that act ... [click to read more]

as neurons. The weights among connected layers are encoded in the amplitude of controlled frequency modes that act as pumps. Interaction among these modes for information processing is enabled by non-linear optical processes. Both the matrix multiplication and element-wise activation functions are performed through coherent processes, enabling the direct representation of negative and complex numbers without the use of detectors or digital electronics. Via numerical simulations, we show that our design achieves a performance commensurate with present-day state-of-the-art computational networks on image-classification benchmarks. Our architecture is unique in providing a completely unitary, reversible mode of computation. Additionally, the computational speed increases with the power of the pumps to arbitrarily high rates, as long as the circuitry can sustain the higher optical power.

Many body localization transition with correlated disorder

Zhengyan Darius Shi, Vedika Khemani, Romain Vasseur, Sarang Gopalakrishnan

Phys. Rev. B 106, 144201 (2022)

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, ... [click to read more]

the characteristic scale for these fluctuations is $\sqrt{\ell}$; more generally they scale as $\ell^\gamma$. We discuss both positively correlated disorder ($1/2 < \gamma < 1$) and anticorrelated, or "hyperuniform," disorder ($\gamma < 1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar \emph{et al.} [Phys. Rev. B 102, 125134, (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.

A note on the quasiperiodic many-body localization transition in dimension $d>1$

Utkarsh Agrawal, Romain Vasseur, Sarang Gopalakrishnan

Phys. Rev. B 106, 094206 (2022)

The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to ... [click to read more]

an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable at strong enough quasiperiodic modulations for $d = 2$, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d \geq 3$.

Distinct universality classes of diffusive transport from full counting statistics

Sarang Gopalakrishnan, Alan Morningstar, Romain Vasseur, Vedika Khemani

Physical Review B 109, 024417 (2024)

The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality ... [click to read more]

classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

Integrability breaking in the Rule 54 cellular automaton

Javier Lopez-Piqueres, Sarang Gopalakrishnan, Romain Vasseur

J. Phys. A: Math. Theor. 55 234005 (2022)

Cellular automata have recently attracted a lot of attention as testbeds to explore the emergence of many-body quantum chaos and hydrodynamics. We consider the Rule 54 model, one of the simplest interacting integrable models featuring two species of quasiparticles (solitons), in the presence of an integrability-breaking perturbation that allows solitons ... [click to read more]

to backscatter. We study the onset of thermalization and diffusive hydrodynamics in this model, compute perturbatively the diffusion constant of tracer particles, and comment on its relation to transport coefficients.

Spin-Phonon-Photon Strong Coupling in a Piezomechanical Nanocavity

Hamza Raniwala, Stefan Krastanov, Lisa Hackett, Matt Eichenfield, Dirk R. Englund, Matthew E. Trusheim


We introduce a hybrid tripartite quantum system for strong coupling between a semiconductor spin, a mechanical phonon, and a microwave photon. Consisting of a piezoelectric resonator with an integrated diamond strain concentrator, this system achieves microwave-acoustic and spin-acoustic coupling rates $\sim$MHz or greater, allowing for simultaneous ultra-high cooperativities ($\sim 10^3$ ... [click to read more]

and $\sim 10^2$, respectively). From finite-element modeling and master equation simulations, we estimate photon-to-spin quantum state transfer fidelities exceeding 0.97 based on separately demonstrated device parameters. We anticipate that this device will enable hybrid quantum architectures that leverage the advantages of both superconducting circuits and solid-state spins for information processing, memory, and networking.

A spin-optomechanical quantum interface enabled by an ultrasmall mechanical and optical mode volume cavity

Hamza Raniwala, Stefan Krastanov, Matt Eichenfield, Dirk Englund


We propose a coherent mechanical interface between defect centers in diamond and telecom optical modes. Combining recent developments in spin-mechanical devices and optomechanical crystals, we introduce a 1D diamond nanobeam with embedded mechanical and electric field concentrator with mechanical and optical mode volumes $V_\mathrm{mech}/\Lambda_\mathrm{p}^3\sim 10^{-5}$ and $V_\mathrm{opt}/\lambda^3\sim 10^{-3} $, respectively. ... [click to read more]

By placing a Group IV vacancy in the concentrator we demonstrate exquisitely high spin-mechanical coupling rates approaching 40 MHz, while retaining high acousto-optical couplings. We theoretically show that such a device, used in an entanglement heralding scheme, can provide high-fidelity Bell pairs between quantum repeaters. Using the mechanical interface as an intermediary between the optical and spin subsystems, we are able to directly use telecom optics, bypassing the native wavelength requirements of the spin. As the spin is never optically excited or addressed, we do not suffer from spectral diffusion and can operate at higher temperatures (up to 40 K), limited only by thermal losses. We estimate that based on these metrics, optomechanical devices with high spin-mechanical coupling will be a useful architecture for near-term quantum repeaters.

Field theory of charge sharpening in symmetric monitored quantum circuits

Fergus Barratt, Utkarsh Agrawal, Sarang Gopalakrishnan, David A. Huse, Romain Vasseur, Andrew C. Potter

Phys. Rev. Lett. 129, 120604 (2022)

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge ... [click to read more]

fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions.

Entanglement dynamics in hybrid quantum circuits

Andrew C. Potter, Romain Vasseur

Chapter in "Entanglement in Spin Chains. Quantum Science and Technology", Springer, pages 211-249 (2022)

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy ... [click to read more]

quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods, and to highlight emerging connections between concepts in stat-mech, quantum information and quantum communication theory.

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Nithin Raveendran, Narayanan Rengaswamy, Filip Rozpędek, Ankur Raina, Liang Jiang, Bane Vasić

Quantum 6, 767 (2022)

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on ... [click to read more]

these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder - a hardware-friendly min-sum algorithm (MSA) - utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

Statistical Mechanics Model for Clifford Random Tensor Networks and Monitored Quantum Circuits

Yaodong Li, Romain Vasseur, Matthew P. A. Fisher, Andreas W. W. Ludwig


We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations because all operators commuting with the action of the unitaries on a tensor product arise from permutations of ... [click to read more]

the tensor factors ('Schur-Weyl duality'). For unitaries restricted to the smaller Clifford group, the set of commuting operators, the 'commutant', forming the new 'spin' degrees of freedom, will be larger. We use the recent full characterization of this commutant by Gross et al., Comm. Math. Phys. 385, 1325 (2021), to construct the Clifford statistical mechanics models for on-site Hilbert space dimensions which are powers of a prime number $p$. We show that the Boltzmann weights are invariant under a symmetry group involving orthogonal matrices with entries in the finite number field ${\bf F}_p$. This implies that the symmetry group, and consequently all universal properties of entanglement transitions in Clifford circuits and RTNs will in general depend on, and only on the prime $p$. We show that Clifford monitored circuits with on-site Hilbert space dimension $d=p^M$ are described by percolation in the limits $d \to \infty$ at (a) $p=$ fixed but $M\to \infty$, and at (b) $M= 1$ but $p \to \infty$. In the limit (a) we calculate the effective central charge, and in the limit (b) we derive the following universal minimal cut entanglement entropy $S_A =(\sqrt{3}/\pi)\ln p \ln L_A$ for $d=p$ large at the transition. We verify those predictions numerically, and present extensive numerical results for critical exponents at the transition in monitored Clifford circuits for prime number on-site Hilbert space dimension $d=p$ for a variety of different values of $p$, and find that they approach percolation values at large $p$.

Controlled-Phase Gate by Dynamic Coupling of Photons to a Two-Level Emitter

Stefan Krastanov, Kurt Jacobs, Gerald Gilbert, Dirk R. Englund, Mikkel Heuck

npj Quantum Information volume 8, Article number: 103 (2022)

We propose an architecture for achieving high-fidelity deterministic quantum logic gates on dual-rail encoded photonic qubits by letting photons interact with a two-level emitter (TLE) inside an optical cavity. The photon wave packets that define the qubit are preserved after the interaction due to a quantum control process that actively ... [click to read more]

loads and unloads the photons from the cavity and dynamically alters their effective coupling to the TLE. The controls rely on nonlinear wave mixing between cavity modes enhanced by strong externally modulated electromagnetic fields or on AC Stark shifts of the TLE transition energy. We numerically investigate the effect of imperfections in terms of loss and dephasing of the TLE as well as control field miscalibration. Our results suggest that III-V quantum dots in GaAs membranes is a promising platform for photonic quantum information processing.

Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

Proc. Nat. Acad. Sci. 119 (34) e2202823119, (2022)

We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large ... [click to read more]

finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is generically not perturbative in the integrability breaking strength.

Distance-Independent Entanglement Generation in a Quantum Network using Space-Time Multiplexed Greenberger-Horne-Zeilinger (GHZ) Measurements

Ashlesha Patil, Joshua I. Jacobson, Emily van Milligen, Don Towsley, Saikat Guha


In a quantum network that successfully creates links, shared Bell states between neighboring repeater nodes, with probability $p$ in each time slot, and performs Bell State Measurements at nodes with success probability $q<1$, the end to end entanglement generation rate drops exponentially with the distance between consumers, despite multi-path routing. ... [click to read more]

If repeaters can perform multi-qubit projective measurements in the GHZ basis that succeed with probability $q$, the rate does not change with distance in a certain $(p,q)$ region, but decays exponentially outside. This region where the distance independent rate occurs is the supercritical region of a new percolation problem. We extend this GHZ protocol to incorporate a time-multiplexing blocklength $k$, the number of time slots over which a repeater can mix-and-match successful links to perform fusion on. As $k$ increases, the supercritical region expands. For a given $(p,q)$, the entanglement rate initially increases with $k$, and once inside the supercritical region for a high enough $k$, it decays as $1/k$ GHZ states per time slot. When memory coherence time exponentially distributed with mean $\mu$ is incorporated, it is seen that increasing $k$ does not indefinitely increase the supercritical region; it has a hard $\mu$ dependent limit. Finally, we find that incorporating space-division multiplexing, i.e., running the above protocol independently in up to $d$ disconnected network regions, where $d$ is the network's node degree, one can go beyond the 1 GHZ state per time slot rate that the above randomized local link-state protocol cannot surpass. As $(p,q)$ increases, one can approach the ultimate min-cut entanglement generation capacity of $d$ GHZ states per slot.

Subdiffusion and many-body quantum chaos with kinetic constraints

Hansveer Singh, Brayden Ware, Romain Vasseur, Aaron J. Friedman

Phys. Rev. Lett. 127, 230602 (2021)

We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian$-$or equivalently, a ... [click to read more]

transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{\text{Th}}$, determined by the spectral form factor, to transport properties and linear response correlators. Using tensor network methods, we determine the dynamical exponent, $z$, for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with 'Fredkin constraints' exhibit anomalous transport with dynamical exponent $z \simeq 8/3$.

Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits

Utkarsh Agrawal, Aidan Zabalo, Kun Chen, Justin H. Wilson, Andrew C. Potter, J. H. Pixley, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. X 12, 041002 2022

Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of ... [click to read more]

exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while R\'enyi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R\'enyi entropies grow ballistically with time $\sim t$. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively-stabilized symmetry-breaking and topological orders.

Realizing a dynamical topological phase in a trapped-ion quantum simulator

Philipp T. Dumitrescu, Justin Bohnet, John Gaebler, Aaron Hankin, David Hayes, Ajesh Kumar, Brian Neyenhuis, Romain Vasseur, Andrew C. Potter

Nature 607, 463-467 (2022)

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and ... [click to read more]

critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information.

Entanglement transitions from restricted Boltzmann machines

Raimel Medina, Romain Vasseur, Maksym Serbyn

Phys. Rev. B 104, 104205 (2021)

The search for novel entangled phases of matter has lead to the recent discovery of a new class of ``entanglement transitions'', exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps ... [click to read more]

onto the free energy cost of inserting a domain wall. In this paper, we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural network-inspired variational Ans\"atze, we investigate under what conditions on the variational parameters these Ans\"atze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite size effects in finite size numerical simulations. Introducing phases with correlations decaying as $1/r^\alpha$ in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent $\alpha$. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.

Operator scaling dimensions and multifractality at measurement-induced transitions

Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, Romain Vasseur, Andreas W. W. Ludwig, Sarang Gopalakrishnan, David A. Huse, J. H. Pixley

Phys. Rev. Lett. 128, 050602 (2022)

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying ... [click to read more]

universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

A quantum walk control plane for distributed quantum computing in quantum networks

Matheus Guedes de Andrade, Wenhan Dai, Saikat Guha, Don Towsley


Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. ... [click to read more]

The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network.

Stability Analysis of a Quantum Network with Max-Weight Scheduling

Thirupathaiah Vasantam, Don Towsley


We study a quantum network that distributes entangled quantum states to multiple sets of users that are connected to the network. Each user is connected to a switch of the network via a link. All the links of the network generate bipartite Bell-state entangled states in each time-slot with certain ... [click to read more]

probabilities, and each end node stores one qubit of the entanglement generated by the link. To create shared entanglements for a set of users, measurement operations are performed on qubits of link-level entanglements on a set of related links, and these operations are probabilistic in nature and are successful with certain probabilities. Requests arrive to the system seeking shared entanglements for different sets of users. Each request is for the creation of shared entanglements for a fixed set of users using link-level entanglements on a fixed set of links. Requests are processed according to First-Come-First-Served service discipline and unserved requests are stored in buffers. Once a request is selected for service, measurement operations are performed on qubits of link-level entanglements on related links to create a shared entanglement. For given set of request arrival rates and link-level entanglement generation rates, we obtain necessary conditions for the stability of queues of requests. In each time-slot, the scheduler has to schedule entanglement swapping operations for different sets of users to stabilize the network. Next, we propose a Max-Weight scheduling policy and show that this policy stabilizes the network for all feasible arrival rates. We also provide numerical results to support our analysis. The analysis of a single quantum switch that creates multipartite entanglements for different sets of users is a special case of our work.

Experimental study of quantum uncertainty from lack of information

Yuan-Yuan Zhao, Filip Rozpędek, Zhibo Hou, Kang-Da Wu, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo

npj Quantum Inf 8, 64 (2022)

Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain comes from the lack of information about the exact state of the system. One may naturally ask, whether the quantum ... [click to read more]

uncertainty is indeed a fully intrinsic property of the quantum theory, or whether similarly to the classical domain lack of knowledge about specific parts of the physical system might be the source of this uncertainty. This question has been addressed in the previous literature where the authors argue that in the entropic formulation of the uncertainty principle that can be illustrated using the, so-called, guessing games, indeed such lack of information has a significant contribution to the arising quantum uncertainty. Here we investigate this issue experimentally by implementing the corresponding two-dimensional and three-dimensional guessing games. Our results confirm that within the guessing-game framework, the quantum uncertainty to a large extent relies on the fact that quantum information determining the key properties of the game is stored in the degrees of freedom that remain inaccessible to the guessing party. Moreover, we offer an experimentally compact method to construct the high-dimensional Fourier gate which is a major building block for various tasks in quantum computation, quantum communication, and quantum metrology.

Operator front broadening in chaotic and integrable quantum chains

Javier Lopez-Piqueres, Brayden Ware, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. B 104, 104307 (2021)

Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from non-interacting systems, it has remained unclear to what extent they can truly diagnose chaotic {\it vs} integrable dynamics ... [click to read more]

in many-body quantum systems. Here, we analyze operator spreading in generic 1D many-body quantum systems using a combination of matrix product operator (MPO) and analytical techniques, focusing on the operator {\em right-weight}. First, we show that while small bond dimension MPOs allow one to capture the exponentially-decaying tail of the operator front, in agreement with earlier results, they lead to significant quantitative and qualitative errors for the actual front -- defined by the maximum of the right-weight. We find that while the operator front broadens diffusively in both integrable and chaotic interacting spin chains, the precise shape and scaling of the height of the front in integrable systems is anomalous for all accessible times. We interpret these results using a quasiparticle picture. This provides a sharp, though rather subtle signature of many-body quantum chaos in the operator front.

Hydrodynamics of weak integrability breaking

Alvise Bastianello, Andrea De Luca, Romain Vasseur

J. Stat. Mech. (2021) 114003

We review recent progress in understanding nearly integrable models within the framework of generalized hydrodynamics (GHD). Integrable systems have infinitely many conserved quantities and stable quasiparticle excitations: when integrability is broken, only a few residual conserved quantities survive, eventually leading to thermalization, chaotic dynamics and conventional hydrodynamics. In this review, ... [click to read more]

we summarize recent efforts to take into account small integrability breaking terms, and describe the transition from GHD to standard hydrodynamics. We discuss the current state of the art, with emphasis on weakly inhomogeneous potentials, generalized Boltzmann equations and collision integrals, as well as bound-state recombination effects. We also identify important open questions for future works.

Hydrodynamic non-linear response of interacting integrable systems

Michele Fava, Sounak Biswas, Sarang Gopalakrishnan, Romain Vasseur, S. A. Parameswaran

Proc. Nat. Acad. Sci. USA 118 (37) e2106945118, (2021)

We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the ... [click to read more]

Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

Stability of superdiffusion in nearly integrable spin chains

Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

Phys. Rev. Lett. 127, 057201 (2021)

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $\sigma(\omega)$, even in systems that are ... [click to read more]

not perfectly integrable. We find, perturbatively, that $ \sigma(\omega) \sim \omega^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $\sigma(\omega) \sim | \log \omega |$ for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

Local integrals of motion and the quasiperiodic many-body localization transition

Hansveer Singh, Brayden Ware, Romain Vasseur, Sarang Gopalakrishnan

Phys. Rev. B 103, 220201 (2021)

We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such ... [click to read more]

time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with this data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations, and has a larger correlation-length critical exponent, than previous studies had found.

Bosonic Random Walk Networks for Graph Learning

Shiv Shankar, Don Towsley


The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph. Recently there has also seen tremendous progress in quantum computing techniques. In this work, we ... [click to read more]

explore applications of multi-particle quantum walks on diffusing information across graphs. Our model is based on learning the operators that govern the dynamics of quantum random walkers on graphs. We demonstrate the effectiveness of our method on classification and regression tasks.

Optically-Heralded Entanglement of Superconducting Systems in Quantum Networks

Stefan Krastanov, Hamza Raniwala, Jeffrey Holzgrafe, Kurt Jacobs, Marko Lončar, Matthew J. Reagor, Dirk R. Englund

Phys. Rev. Lett. 127, 040503 (2021)

Networking superconducting quantum computers is a longstanding challenge in quantum science. The typical approach has been to cascade transducers: converting to optical frequencies at the transmitter and to microwave frequencies at the receiver. However, the small microwave-optical coupling and added noise have proven formidable obstacles. Instead, we propose optical networking ... [click to read more]

via heralding end-to-end entanglement with one detected photon and teleportation. In contrast to cascaded direct transduction, our scheme absorbs the low optical-microwave coupling efficiency into the heralding step, thus breaking the rate-fidelity trade-off. Moreover, this technique unifies and simplifies entanglement generation between superconducting devices and other physical modalities in quantum networks.

Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

Filip Rozpędek, Kyungjoo Noh, Qian Xu, Saikat Guha, Liang Jiang

npj Quantum Inf. 7, 102 (2021)

We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single ... [click to read more]

bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

Purification and Entanglement Routing on Quantum Networks

Michelle Victora, Stefan Krastanov, Alexander Sanchez de la Cerda, Steven Willis, Prineha Narang


We present an approach to purification and entanglement routing on complex quantum network architectures, that is, how a quantum network equipped with imperfect channel fidelities and limited memory storage time can distribute entanglement between users. We explore how network parameters influence the performance of path-finding algorithms necessary for optimizing routing ... [click to read more]

and, in particular, we explore the interplay between the bandwidth of a quantum channels and the choice of purification protocol. Finally, we demonstrate multi-path routing on various network topologies with resource constraints, in an effort to inform future design choices for quantum network configurations. Our work optimizes both the choice of path over the quantum network and the choice of purification schemes used between nodes. We consider not only pair-production rate, but optimize over the fidelity of the delivered entangled state. We introduce effective heuristics enabling fast path-finding algorithms for maximizing entanglement shared between two nodes on a quantum network, with performance comparable to that of a computationally-expensive brute-force path search.

Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices

Stefan Krastanov, Alexander Sanchez de la Cerda, Prineha Narang

Phys. Rev. Research 3, 033164 (2021)

The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell ... [click to read more]

pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elusive. Here we depart from the typical purification paradigm for multipartite states explored in the last twenty years. We present cases where the hardware limitations are taken into account, and surprisingly find that smaller `sacrificial' states, like Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states. This drastically simplifies the requirements and presents a fundamentally new pathway to leverage near term networked quantum hardware.

NetSquid, a NETwork Simulator for QUantum Information using Discrete events

Tim Coopmans, Robert Knegjens, Axel Dahlberg, David Maier, Loek Nijsten, Julio de Oliveira Filho, Martijn Papendrecht, Julian Rabbie, Filip Rozpędek, Matthew Skrzypczyk, Leon Wubben, Walter de Jong, Damian Podareanu, Ariana Torres-Knoop, David Elkouss, Stephanie Wehner

Commun Phys 4, 164 (2021)

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork ... [click to read more]

Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

Perturbative instability of non-ergodic phases in non-Abelian quantum chains

Brayden Ware, Dmitry Abanin, Romain Vasseur

Phys. Rev. B 103, 094203 (2021)

An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group ... [click to read more]

methods predict a partially localized, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). This regime features a tree-like hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative non-ergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and time scales for thermalization: even if such chains eventually thermalize, they can exhibit non-ergodic dynamics up to parametrically long time scales with a non-analytic dependence on disorder strength.

Quantum coding with low-depth random circuits

Michael J. Gullans, Stefan Krastanov, David A. Huse, Liang Jiang, Steven T. Flammia

Phys. Rev. X 11, 031066 (2021)

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in $D\ge 1$ spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, ... [click to read more]

we find strong evidence that a depth $O(\log N)$ random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the optimal erasure threshold, set by the channel capacity, for any $D$. Previous results on random circuits have only shown that $O(N^{1/D})$ depth suffices or that $O(\log^3 N)$ depth suffices for all-to-all connectivity ($D \to \infty$). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the optimal threshold converge to zero with $N$. We find that the requisite depth scales like $O(\log N)$ only for dimensions $D \ge 2$, and that random circuits require $O(\sqrt{N})$ depth for $D=1$. Finally, we introduce an "expurgation" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into additional stabilizers or gauge operators. With such targeted measurements, we can achieve sub-logarithmic depth in $D\ge 2$ below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in $D=2$ dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications.

Distributing Graph States Across Quantum Networks

Alex Fischer, Don Towsley


Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which local operations are free-and EPR pairs shared between nodes that can continually be generated. We ... [click to read more]

prove upper bounds for our approach on the number of EPR pairs consumed, number of timesteps taken, and amount of classical communication required, all of which are equal to or better than that of prior work. We also reduce the problem of minimizing the number of timesteps taken to distribute a graph state using our approach to a network flow problem having polynomial time complexity.

Superuniversality of superdiffusion

Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

Phys. Rev. X 11, 031023 (2021)

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model invariant under a ... [click to read more]

global non-abelian simple Lie group $G$, we find that finite-temperature transport of Noether charges associated with symmetry $G$ in thermal states that are invariant under $G$ is universally superdiffusive and characterized by dynamical exponent $z = 3/2$. This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: we accordingly dub it as superuniversal. The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

Unboxing Quantum Black Box Models: Learning Non-Markovian Dynamics

Stefan Krastanov, Kade Head-Marsden, Sisi Zhou, Steven T. Flammia, Liang Jiang, Prineha Narang


Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete superoperators, or they employ machine learning methods, neither of which provide physical insight into the dynamics of the quantum ... [click to read more]

system. To circumvent this limitation, we design learning architectures that explicitly encode physical constraints like the properties of completely-positive trace-preserving maps in a differential form. This method preserves the versatility of the machine learning approach without sacrificing the efficiency and fidelity of traditional parameter estimation methods. Our approach provides the physical interpretability that machine learning and opaque superoperators lack. Moreover, it is aware of the underlying continuous dynamics typically disregarded by superoperator-based tomography. This paradigm paves the way to noise-aware optimal quantum control and opens a path to exploiting the bath as a control and error mitigation resource.

Topological edge modes without symmetry in quasiperiodically driven spin chains

Aaron J. Friedman, Brayden Ware, Romain Vasseur, Andrew C. Potter

Phys. Rev. B 105, 115117 (2022)

We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the ... [click to read more]

edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

Quantum criticality in the 2d quasiperiodic Potts model

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 125, 265702 (2020)

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic $q$-state Potts model in $2+1d$. Using a controlled real-space renormalization group approach, we find ... [click to read more]

that the critical behavior is largely independent of $q$, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be $\nu=1$, saturating a modified version of the Harris-Luck criterion.

Superuniversality from disorder at two-dimensional topological phase transitions

Byungmin Kang, S. A. Parameswaran, Andrew C. Potter, Romain Vasseur, Snir Gazit

Phys. Rev. B 102, 224204 (2020)

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial ... [click to read more]

mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

Topological and symmetry-enriched random quantum critical points

Carlos M. Duque, Hong-Ye Hu, Yi-Zhuang You, Vedika Khemani, Ruben Verresen, Romain Vasseur

Phys. Rev. B 103, 100207 (2021)

We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of ... [click to read more]

such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems.

Hydrodynamics of nonintegrable systems from a relaxation-time approximation

Javier Lopez-Piqueres, Brayden Ware, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. B 103, 060302 (2021)

We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is based on a generalized relaxation-time approximation; it gives a simple, but surprisingly accurate, prescription for computing nonequilibrium transport ... [click to read more]

even in strongly interacting systems. This approximation reproduces the crossover from generalized to conventional hydrodynamics in interacting one-dimensional Bose gases with integrability-breaking perturbations, both with and without momentum conservation. It also predicts the hydrodynamics of chaotic quantum spin chains, in good agreement with matrix product operator calculations.

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Michele Fava, Brayden Ware, Sarang Gopalakrishnan, Romain Vasseur, S. A. Parameswaran

Phys. Rev. B 102, 115121 (2020)

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers ... [click to read more]

between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, that are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is sub-ballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via $x\sim t^{2/3}$) along both lines and at the $SO(4)$-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Kade Head-Marsden, Stefan Krastanov, David A. Mazziotti, Prineha Narang

Phys. Rev. Research 3, 013182 (2021)

With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum algorithms for the treatment of open quantum systems (OQSs) have remained under-explored, in part due to the ... [click to read more]

inherent challenges of mapping non-unitary evolution into the framework of unitary gates. Evolving an open system unitarily necessitates dilation into a new effective system to incorporate critical environmental degrees of freedom. In this context, we present and validate a new quantum algorithm to treat non-Markovian dynamics in OQSs built on the Ensemble of Lindblad's Trajectories approach, invoking the Sz.-Nagy dilation theorem. Here we demonstrate our algorithm on the Jaynes-Cummings model in the strong coupling and detuned regimes, relevant in quantum optics and driven quantum systems studies. This algorithm, a key step towards generalized modeling of non-Markovian dynamics on a noisy-quantum device, captures a broad class of dynamics and opens up a new direction in OQS problems.

Efficient cavity control with SNAP gates

Thomas Fösel, Stefan Krastanov, Florian Marquardt, Liang Jiang


Microwave cavities coupled to superconducting qubits have been demonstrated to be a promising platform for quantum information processing. A major challenge in this setup is to realize universal control over the cavity. A promising approach are selective number-dependent arbitrary phase (SNAP) gates combined with cavity displacements. It has been proven ... [click to read more]

that this is a universal gate set, but a central question remained open so far: how can a given target operation be realized efficiently with a sequence of these operations. In this work, we present a practical scheme to address this problem. It involves a hierarchical strategy to insert new gates into a sequence, followed by a co-optimization of the control parameters, which generates short high-fidelity sequences. For a broad range of experimentally relevant applications, we find that they can be implemented with 3 to 4 SNAP gates, compared to up to 50 with previously known techniques.

Superdiffusion from emergent classical solitons in quantum spin chains

Jacopo De Nardis, Sarang Gopalakrishnan, Enej Ilievski, Romain Vasseur

Phys. Rev. Lett. 125, 070601 (2020)

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; ... [click to read more]

the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

Covert Cycle Stealing in a Single FIFO Server

Bo Jiang, Philippe Nain, Don Towsley


Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: what is the number of jobs that she ... [click to read more]

can receive covertly, i.e. without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates $\mu_1$ and $\mu_2$, we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles : over $n$ busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of $\mathcal{O}(\sqrt{n})$ when $\mu_1 < 2\mu_2$, $\mathcal{O}(\sqrt{n/\log n})$ when $\mu_1 = 2\mu_2$, and $\mathcal{O}(n^{\mu_2/\mu_1})$ when $\mu_1 > 2\mu_2$. When both Willie and Alice jobs have general service times we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

Mean-field entanglement transitions in random tree tensor networks

Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur

Phys. Rev. B 102, 064202 (2020)

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As ... [click to read more]

a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

Key rates for quantum key distribution protocols with asymmetric noise

Gláucia Murta, Filip Rozpędek, Jérémy Ribeiro, David Elkouss, Stephanie Wehner

Phys. Rev. A 101, 062321 (2020)

We consider the asymptotic key rates achieved in the simplest quantum key distribution protocols, namely the BB84 and the six-state protocols, when non-uniform noise is present in the system. We first observe that higher qubit error rates do not necessarily imply lower key rates. Secondly, we consider protocols with advantage ... [click to read more]

distillation and show that it can be advantageous to use the basis with higher quantum bit error rate for the key generation. We then discuss the relation between advantage distillation and entanglement distillation protocols. We show that applying advantage distillation to a string of bits formed by the outcomes of measurements in the basis with higher quantum bit error rate is closely connected to the two-to-one entanglement distillation protocol DEJMPS. Finally, we discuss the implications of these results for implementations of quantum key distribution.

Room-Temperature Photonic Logical Qubits via Second-Order Nonlinearities

Stefan Krastanov, Mikkel Heuck, Jeffrey H. Shapiro, Prineha Narang, Dirk R. Englund, Kurt Jacobs

Nature Communications volume 12, Article number: 191 (2021)

Recent progress in nonlinear optical materials and microresonators has brought quantum computing with bulk optical nonlinearities into the realm of possibility. This platform is of great interest, not only because photonics is an obvious choice for quantum networks, but also because it may be the only feasible route to quantum ... [click to read more]

information processing at room temperature. We introduce a paradigm for room-temperature photonic quantum logic that significantly simplifies the realization of various quantum circuits, and in particular, of error correction. It uses only the strongest available bulk nonlinearity, namely the $\chi^{(2)}$ nonlinear susceptibility. The key element is a three-mode resonator that implements programmable bosonic quantum logic gates. We show that just two of these elements suffice for a complete, compact error-correction circuit on a bosonic code, without the need for measurement or feed-forward control. An extrapolation of current progress in nonlinear optical materials and photonic circuits indicates that such circuitry should be achievable within the next decade.

Integrated multi-wavelength control of an ion qubit

Robert J. Niffenegger, Jules Stuart, Cheryl Sorace-Agaskar, Dave Kharas, Suraj Bramhavar, Colin D. Bruzewicz, William Loh, Ryan T. Maxson, Robert McConnell, David Reens, Gavin N. West, Jeremy M. Sage, John Chiaverini

Nature 586, 538-542 (2020)

Monolithic integration of control technologies for atomic systems is a promising route to the development of quantum computers and portable quantum sensors. Trapped atomic ions form the basis of high-fidelity quantum information processors and high-accuracy optical clocks. However, current implementations rely on free-space optics for ion control, which limits their ... [click to read more]

portability and scalability. Here we demonstrate a surface-electrode ion-trap chip using integrated waveguides and grating couplers, which delivers all the wavelengths of light required for ionization, cooling, coherent operations, and quantum-state preparation and detection of Sr+ qubits. Laser light from violet to infrared is coupled onto the chip via an optical-fiber array, creating an inherently stable optical path, which we use to demonstrate qubit coherence that is resilient to platform vibrations. This demonstration of CMOS-compatible integrated-photonic surface-trap fabrication, robust packaging, and enhanced qubit coherence is a key advance in the development of portable trapped-ion quantum sensors and clocks, providing a way toward the complete, individual control of larger numbers of ions in quantum information processing systems.

Diffusive hydrodynamics from integrability breaking

Aaron J. Friedman, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. B 101, 180302 (2020)

We describe the crossover from generalized hydrodynamics to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we derive a compact ... [click to read more]

and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.

Distinguishing localization from chaos: challenges in finite-size systems

D. A. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. A. Parameswaran, F. Pollmann, A. C. Potter, M. Serbyn, R. Vasseur

Annals of Physics 427, 168415 (2021)

We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected ... [click to read more]

by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [\v{S}untajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.

Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

Phys. Rev. B 101, 224415 (2020)

In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $\Delta = \cos \pi \lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for ... [click to read more]

generic irrational values of $\lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $\sigma(\omega) \sim 1/\sqrt{\omega}$; anomalous response occurs because quasiparticles undergo L\'evy flights. For rational values of $\lambda$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $\Delta=1$, spin transport is superdiffusive with $\sigma(\omega) \sim \omega^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

Measurement-induced criticality in random quantum circuits

Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, Andreas W. W. Ludwig

Phys. Rev. B 101, 104302 (2020)

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical mechanics model. In this language, the area- to volume-law entanglement transition can ... [click to read more]

be interpreted as an ordering transition in the statistical mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the $n$th R\'enyi entropies for $n \geq 1$ in this limit using relatively recent results for conformal field theory describing the critical theory of 2D percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. We also comment on the relation to the entanglement transition in Random Tensor Networks, studied previously in Ref. 1.

Universality and Quantum Criticality in Quasiperiodic Spin Chains

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur

Nature Communication 11, 2225 (2020)

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a ... [click to read more]

wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization group transformation. These discrete sequences are therefore fixed points of a \emph{functional} renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

Distributed Routing in a Quantum Internet

Kaushik Chakraborty, Filip Rozpedek, Axel Dahlberg, Stephanie Wehner


We develop new routing algorithms for a quantum network with noisy quantum devices such that each can store a small number of qubits. We thereby consider two models for the operation of such a network. The first is a continuous model, in which entanglement between a subset of the nodes ... [click to read more]

is produced continuously in the background. This can in principle allows the rapid creation of entanglement between more distant nodes using the already pre-generated entanglement pairs in the network. The second is an on-demand model, where entanglement production does not commence before a request is made. Our objective is to find protocols, that minimise the latency of the network to serve a request to create entanglement between two distant nodes in the network. We propose three routing algorithms and analytically show that as expected when there is only a single request in the network, then employing them on the continuous model yields a lower latency than on the on-demand one. We study the performance of the routing algorithms in a ring, grid, and recursively generated network topologies. We also give an analytical upper bound on the number of entanglement swap operations the nodes need to perform for routing entangled links between a source and a destination yielding a lower bound on the end to end fidelity of the shared entangled state. We proceed to study the case of multiple concurrent requests and show that in some of the scenarios the on-demand model can outperform the continuous one. Using numerical simulations on ring and grid networks we also study the behaviour of the latency of all the routing algorithms. We observe that the proposed routing algorithms behave far better than the existing classical greedy routing algorithm. The simulations also help to understand the advantages and disadvantages of different types of continuous models for different types of demands.

Integrable many-body quantum Floquet-Thouless pumps

Aaron J. Friedman, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 123, 170603 (2019)

We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model, and show that these take on a particularly simple ... [click to read more]

form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem to be possible in other interacting integrable systems. This model illustrates the existence a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.

Anomalous relaxation and the high-temperature structure factor of XXZ spin chains

Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

PNAS 116 (33)16250-16255 (2019)

We compute the spin structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to $s$-spin magnon bound ... [click to read more]

states (`strings') of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the crossover to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.

Quantum Networks For Open Science

Thomas Ndousse-Fetter, Nicholas Peters, Warren Grice, Prem Kumar, Tom Chapuran, Saikat Guha, Scott Hamilton, Inder Monga, Ray Newell, Andrei Nomerotski, Don Towsley, Ben Yoo


The United States Department of Energy convened the Quantum Networks for Open Science (QNOS) Workshop in September 2018. The workshop was primarily focused on quantum networks optimized for scientific applications with the expectation that the resulting quantum networks could be extended to lay the groundwork for a generalized network that ... [click to read more]

will evolve into a quantum internet.

A Link Layer Protocol for Quantum Networks

Axel Dahlberg, Matthew Skrzypczyk, Tim Coopmans, Leon Wubben, Filip Rozpędek, Matteo Pompili, Arian Stolk, Przemysław Pawełczak, Robert Knegjens, Julio de Oliveira Filho, Ronald Hanson, Stephanie Wehner

SIGCOMM '19 Proceedings of the ACM Special Interest Group on Data Communication (2019) 159-173

Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a fully fledged quantum internet system. We propose a functional allocation of a quantum network stack and construct the first physical and link ... [click to read more]

layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). Using a purpose built discrete-event simulator for quantum networks, we examine the robustness and performance of our protocol using extensive simulations on a super-computing cluster. We perform a full implementation of our protocol, where we successfully validate the physical simulation model against data gathered from the NV hardware. We first observe that our protocol is robust even in a regime of exaggerated losses of classical control messages with only little impact on the performance of the system.We proceed to study the performance of our protocols for 169 distinct simulation scenarios, including tradeoffs between traditional performance metrics such as throughput and the quality of entanglement. Finally, we initiate the study of quantum network scheduling strategies to optimize protocol performance for different use cases.

On the Stochastic Analysis of a Quantum Entanglement Switch

Gayane Vardoyan, Saikat Guha, Philippe Nain, Don Towsley

IEEE Transactions on Quantum Engineering 2021

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate ... [click to read more]

to use a discrete-time Markov chain (DTMC) to model such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. B 99, 174203 (2019)

We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to ... [click to read more]

disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clean integrable systems. This implies that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wavefunctions are delocalized and a phase in which low-energy wavefunctions are quasi-localized (in a sense we specify). Both phases have ballistic transport; however, in the quasi-localized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.

Quantum Brownian motion in a quasiperiodic potential

Aaron J Friedman, Romain Vasseur, Austen Lamacraft, S. A. Parameswaran

Phys. Rev. B 100, 060301 (2019)

We consider a quantum particle subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. In a periodic potential the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is ... [click to read more]

infinitesimal. Using the renormalization group, we determine how the effective localization length depends on the dissipation. We show that {a similar problem can emerge in} the strong-coupling limit of a mobile impurity moving in a periodic lattice and immersed in a one-dimensional quantum gas.

Stochastic Estimation of Dynamical Variables

Stefan Krastanov, Sisi Zhou, Steven T. Flammia, Liang Jiang

Quantum Science and Technology, Volume 4 (2019), 035003

Estimating the parameters governing the dynamics of a system is a prerequisite for its optimal control. We present a simple but powerful method that we call STEADY, for STochastic Estimation algorithm for DYnamical variables, to estimate the Hamiltonian (or Lindbladian) governing a quantum system of a few qubits. STEADY makes ... [click to read more]

efficient use of all measurements and its performance scales as the information-theoretic limits for such an estimator. Importantly, it is inherently robust to state preparation and measurement errors. It is not limited to evaluating only a fixed set of possible gates, rather it estimates the complete Hamiltonian of the system. The estimator is applicable to any Hamiltonian that can be written as a piecewise-differentiable function and it can easily include estimators for the non-unitary parameters as well. At the heart of our approach is a stochastic gradient descent over the difference between experimental measurement and model prediction.

Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains

Sarang Gopalakrishnan, Romain Vasseur

Phys. Rev. Lett. 122, 127202 (2019)

We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics combined with Gaussian fluctuations: we find that it diverges, and show that a self-consistent treatment of this divergence ... [click to read more]

gives superdiffusion, with an effective time-dependent diffusion constant that scales as $D(t) \sim t^{1/3}$. This exponent had previously been observed in large-scale numerical simulations, but had not been theoretically explained. We briefly discuss XXZ models with easy-axis anisotropy $\Delta > 1$. Our method gives closed-form expressions for the diffusion constant $D$ in the infinite-temperature limit for all $\Delta > 1$. We find that $D$ saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as $D \sim (\Delta - 1)^{-1/2}$.

Kosterlitz-Thouless scaling at many-body localization phase transitions

Philipp T. Dumitrescu, Anna Goremykina, Siddharth A. Parameswaran, Maksym Serbyn, Romain Vasseur

Phys. Rev. B 99, 094205 (2019)

We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a 'quantum avalanche'. We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, ... [click to read more]

we identify the scaling variables as the density of thermal regions and the lengthscale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent $\alpha_c=2$, and continuously varying exponents in the MBL phase consistent with the KT picture.

Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

Sarang Gopalakrishnan, David A. Huse, Vedika Khemani, Romain Vasseur

Phys. Rev. B 98, 220303 (2018)

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other ... [click to read more]

quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.

Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission

Filip Rozpędek, Raja Yehia, Kenneth Goodenough, Maximilian Ruf, Peter C. Humphreys, Ronald Hanson, Stephanie Wehner, David Elkouss

Phys. Rev. A 99, 052330 (2019)

Quantum channels enable the implementation of communication tasks inaccessible to their classical counterparts. The most famous example is the distribution of secret key. However, in the absence of quantum repeaters, the rate at which these tasks can be performed is dictated by the losses in the quantum channel. In practice, ... [click to read more]

channel losses have limited the reach of quantum protocols to short distances. Quantum repeaters have the potential to significantly increase the rates and reach beyond the limits of direct transmission. However, no experimental implementation has overcome the direct transmission threshold. Here, we propose three quantum repeater schemes and assess their ability to generate secret key when implemented on a setup using nitrogen-vacancy (NV) centers in diamond with near-term experimental parameters. We find that one of these schemes - the so-called single-photon scheme, requiring no quantum storage - has the ability to surpass the capacity - the highest secret-key rate achievable with direct transmission - by a factor of 7 for a distance of approximately 9.2 km with near-term parameters, establishing it as a prime candidate for the first experimental realization of a quantum repeater.

Strong-Disorder Renormalization Group for Periodically Driven Systems

William Berdanier, Michael Kolodrubetz, S. A. Parameswaran, Romain Vasseur

Phys. Rev. B 98, 174203 (2018)

Quenched randomness can lead to robust non-equilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder and discrete time-translation symmetry. We introduce a real-space renormalization group approach, asymptotically exact in the strong-disorder limit, and ... [click to read more]

exemplify its use on the periodically driven interacting quantum Ising model. We analyze the universal physics near the critical lines and multicritical point of this model, and demonstrate the robustness of our results to the inclusion of weak interactions.

Entanglement Transitions from Holographic Random Tensor Networks

Romain Vasseur, Andrew C. Potter, Yi-Zhuang You, Andreas W. W. Ludwig

Phys. Rev. B 100, 134203 (2019)

We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low ... [click to read more]

entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the "holographic" boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

Analytically solvable renormalization group for the many-body localization transition

Anna Goremykina, Romain Vasseur, Maksym Serbyn

Phys. Rev. Lett. 122, 040601 (2019)

We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, ... [click to read more]

reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.

Optimizing practical entanglement distillation

Filip Rozpędek, Thomas Schiet, Le Phuc Thinh, David Elkouss, Andrew C. Doherty, Stephanie Wehner

Phys. Rev. A 97, 062333 (2018)

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a tradeoff between the fidelity to the target state, and the probability of successful distillation. Exploiting such tradeoffs is of interest in ... [click to read more]

the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss (EPL) entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.

Floquet Quantum Criticality

William Berdanier, Michael Kolodrubetz, S. A. Parameswaran, Romain Vasseur

PNAS 115 (38) 9491-9496 (2018)

We study transitions between distinct phases of one-dimensional periodically driven (Floquet) systems. We argue that these are generically controlled by infinite-randomness fixed points of a strong-disorder renormalization group procedure. Working in the fermionic representation of the prototypical Floquet Ising chain, we leverage infinite randomness physics to provide a simple description ... [click to read more]

of Floquet (multi)criticality in terms of a new type of domain wall associated with time-translational symmetry-breaking and the formation of `Floquet time crystals'. We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.

Many-body localization, symmetry, and topology

S. A. Parameswaran, Romain Vasseur

Rep. Prog. Phys. 81, 082501 (2018)

We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order ... [click to read more]

are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

Optimized Entanglement Purification

Stefan Krastanov, Victor V. Albert, Liang Jiang

Quantum 3, 123 (2019)

We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical ... [click to read more]

study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the effects of finite resources and imperfect local operations - phenomena neglected in the usual asymptotic approach to the problem. The choice of the building blocks permitted in the construction of the circuits is based on a thorough enumeration of the local Clifford operations that act as permutations on the basis of Bell states.

Topological Luttinger Liquids from Decorated Domain Walls

Daniel E Parker, Thomas Scaffidi, Romain Vasseur

Phys. Rev. B 97, 165114 (2018)

We introduce a systematic construction of a gapless symmetry protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids. The resulting strongly interacting phases provide a concrete example of a gapless symmetry protected topological (gSPT) phase with robust symmetry-protected edge modes. Using boundary conformal field theory ... [click to read more]

arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly-coupled renormalization group fixed point. Our results are checked against extensive density matrix renormalization group calculations.

Sparse Diffusion-Convolutional Neural Networks

James Atwood, Siddharth Pal, Don Towsley, Ananthram Swami


The predictive power and overall computational efficiency of Diffusion-convolutional neural networks make them an attractive choice for node classification tasks. However, a naive dense-tensor-based implementation of DCNNs leads to $\mathcal{O}(N^2)$ memory complexity which is prohibitive for large graphs. In this paper, we introduce a simple method for thresholding input graphs ... [click to read more]

that provably reduces memory requirements of DCNNs to O(N) (i.e. linear in the number of nodes in the input) without significantly affecting predictive performance.

Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains

Philipp T. Dumitrescu, Romain Vasseur, Andrew C. Potter

Phys. Rev. Lett. 120, 070602 (2018)

We simulate the dynamics of a disordered interacting spin chain subject to a quasi-periodic time-dependent drive, corresponding to a stroboscopic Fibonacci sequence of two distinct Hamiltonians. Exploiting the recursive drive structure, we can efficiently simulate exponentially long times. After an initial transient, the system exhibits a long-lived glassy regime characterized ... [click to read more]

by a logarithmically slow growth of entanglement and decay of correlations analogous to the dynamics at the many-body delocalization transition. Ultimately, at long time-scales, which diverge exponentially for weak or rapid drives, the system thermalizes to infinite temperature. The slow relaxation enables metastable dynamical phases, exemplified by a "time quasi-crystal" in which spins exhibit persistent oscillations with a distinct quasi-periodic pattern from that of the drive. We show that in contrast with Floquet systems, a high-frequency expansion strictly breaks down above fourth order, and fails to produce an effective static Hamiltonian that would capture the pre-thermal glassy relaxation.

Localization-protected order in spin chains with non-Abelian discrete symmetries

Aaron J. Friedman, Romain Vasseur, Andrew C. Potter, S. A. Parameswaran

Phys. Rev. B 98, 064203 (2018)

We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we ... [click to read more]

find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the ${\mathbb{Z}_3}$ clock symmetry or a ${\mathbb{Z}_2}$ chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.

Deep Neural Network Probabilistic Decoder for Stabilizer Codes

Stefan Krastanov, Liang Jiang

Scientific Reports 7, Article number: 11003 (2017)

Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a decoder that employs a neural network to calculate the conditional distribution, then sample from the ... [click to read more]

distribution - the sample will be the predicted error for the given syndrome. We present an implementation of such an algorithm that can be applied to any stabilizer code. Testing it on the toric code, it has higher threshold than a number of known decoders thanks to naturally finding the most probable error and accounting for correlations between errors.

On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

Jonathan Belletête, Azat M. Gainutdinov, Jesper L. Jacobsen, Hubert Saleur, Romain Vasseur

J. Phys A: Math. Theor. 50 (2017) 484002

The relationship between bulk and boundary properties is one of the founding features of (Rational) Conformal Field Theory. Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice models. We focus on models based on the Temperley-Lieb algebra, and use ... [click to read more]

the concept of braid translation, which is a natural way to close an open spin chain by adding an interaction between the first and last spins using braiding to bring them next to each other. The interaction thus obtained is in general non-local, but has the key feature that it is expressed solely in terms of the algebra for the open spin chain - the ordinary Temperley-Lieb algebra and its blob algebra generalization. This is in contrast with the usual periodic spin chains which involve only local interactions, and are described by the periodic TL algebra. We show that for the Restricted Solid-On-Solid models, which are known to be described by minimal unitary CFTs in the continuum limit, the braid translation in fact does provide the ordinary periodic model starting from the open model with fixed boundary conditions on the two sides of the strip. This statement has a precise mathematical formulation, which is a pull-back map between irreducible modules of, respectively, the blob algebra and the affine TL algebra. We then turn to the same kind of analysis for two models whose continuum limits are Logarithmic CFTs - the alternating gl(1|1) and sl(2|1) spin chains. We find that the result for minimal models does not hold any longer: braid translation of the relevant TL modules does not give rise to the modules known to be present in the periodic chains. In the gl(1|1) case, the content in terms of the irreducibles is the same, as well as the spectrum, but the detailed structure (like logarithmic coupling) is profoundly different. This carries over to the continuum limit.

Gapless Symmetry Protected Topological Order

Thomas Scaffidi, Daniel E. Parker, Romain Vasseur

Phys. Rev. X 7, 041048 (2017)

We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls "decorated" with dimension $(d-1)$ SPT systems. Using a combination of field theory ... [click to read more]

and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry-broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wavefunctions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.

Parameter regimes for a single sequential quantum repeater

Filip Rozpędek, Kenneth Goodenough, Jérémy Ribeiro, Norbert Kalb, Valentina Caprara Vivoli, Andreas Reiserer, Ronald Hanson, Stephanie Wehner, David Elkouss

F Rozp\k{e}dek et al 2018 Quantum Sci. Technol. 3 034002

Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by ... [click to read more]

the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters.

Solvable Hydrodynamics of Quantum Integrable Systems

Vir B. Bulchandani, Romain Vasseur, Christoph Karrasch, Joel E. Moore

Phys. Rev. Lett. 119, 220604 (2017)

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study time evolution from local equilibria in such ... [click to read more]

models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudo-momentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Non-scalar operators for the Potts model in arbitrary dimension

Romain Couvreur, Jesper Lykke Jacobsen, Romain Vasseur


We investigate the operator content of the Q-state Potts model in arbitrary dimension, using the representation theory of the symmetric group. In particular we construct all possible tensors acting on N spins, corresponding to given symmetries under $S_Q$ and $S_N$, in terms of representations involving any Young diagram. These operators ... [click to read more]

transform non-trivially under the group of spatial rotations, with a definite conformal spin. The two-point correlation functions are then computed, and their physical interpretation is given in terms of Fortuin-Kasteleyn clusters propagating between two neighbourhoods of each N spins. In two dimensions, we obtain analytically the critical exponent corresponding to each operator. In the simplest and physically most relevant cases, we confirm the values of the critical exponent and the conformal spin by numerical measurements, using both Monte Carlo simulations and transfer matrix diagonalisations. Our classification partially provides the structure of Jordan cells of the dilatation operator in arbitrary dimensions, which in turn gives rise to logarithmic correlation functions.

Healing of Defects in Random Antiferromagnetic Spin Chains

Romain Vasseur, Arash Roshani, Stephan Haas, Hubert Saleur

EPL 119 50004 (2017)

We study the effects of a weakened link in random antiferromagnetic spin chains. We show that healing occurs, and that homogeneity is restored at low energy, in a way that is qualitatively similar to the fate of impurities in clean ferromagnetic spin chains, or in Luttinger liquids with attractive interactions. ... [click to read more]

Healing in the random case occurs even without interactions, and is characteristic of the random singlet phase. Using real space renormalization group and exact diagonalization methods, we characterize this universal healing crossover by studying the entanglement across the weak link. We identify a crossover healing length $L^*$ that separates a regime where the system is cut in half by the weak link from a fixed point where the spin chain is healed. Our results open the way to the study of impurity physics in disordered spin chains.

Entanglement Entropy in Excited States of the Quantum Lifshitz Model

Daniel E. Parker, Romain Vasseur, Joel E. Moore

Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 25 (2017)

We investigate the entanglement properties of an infinite class of excited states in the quantum Lifshitz model (QLM). The presence of a conformal quantum critical point in the QLM makes it unusually tractable for a model above one spatial dimension, enabling the ground state entanglement entropy for an arbitrary domain ... [click to read more]

to be expressed in terms of geometrical and topological quantities. Here we extend this result to excited states and find that the entanglement can be naturally written in terms of quantities which we dub "entanglement propagator amplitudes" (EPAs). EPAs are geometrical probabilities that we explicitly calculate and interpret. A comparison of lattice and continuum results demonstrates that EPAs are universal. This work shows that the QLM is an example of a 2+1d field theory where the universal behavior of excited-state entanglement may be computed analytically.

Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain

Vir B. Bulchandani, Romain Vasseur, Christoph Karrasch, Joel E. Moore

Phys. Rev. B 97, 045407 (2018)

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic ... [click to read more]

theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe non-equilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

Multiplexed entanglement generation over quantum networks using multi-qubit nodes

Suzanne B. van Dam, Peter C. Humphreys, Filip Rozpędek, Stephanie Wehner, Ronald Hanson


Quantum networks distributed over distances greater than a few kilometers will be limited by the time required for information to propagate between nodes. We analyze protocols that are able to circumvent this bottleneck by employing multi-qubit nodes and multiplexing. For each protocol, we investigate the key network parameters that determine ... [click to read more]

its performance. We model achievable entangling rates based on the anticipated near-term performance of nitrogen-vacancy centres and other promising network platforms. This analysis allows us to compare the potential of the proposed multiplexed protocols in different regimes. Moreover, by identifying the gains that may be achieved by improving particular network parameters, our analysis suggests the most promising avenues for research and development of prototype quantum networks.

Universal Entanglement Dynamics following a Local Quench

Romain Vasseur, Hubert Saleur

SciPost Phys. 3, 001 (2017)

We study the time dependence of the entanglement between two quantum wires after suddenly connecting them via tunneling through an impurity. The result at large times is given by the well known formula $S(t) \approx {1\over 3}\ln {t}$. We show that the intermediate time regime can be described by a ... [click to read more]

universal cross-over formula $S=F(tT_K)$, where $T_K$ is the crossover (Kondo) temperature: the function $F$ describes the dynamical "healing" of the system at large times. We discuss how to obtain analytic information about $F$ in the case of an integrable quantum impurity problem using the massless Form-Factors formalism for twist and boundary condition changing operators. Our results are confirmed by density matrix renormalization group calculations and exact free fermion numerics.

Floquet Dynamics of Boundary-Driven Systems at Criticality

William Berdanier, Michael Kolodrubetz, Romain Vasseur, Joel E. Moore

Phys. Rev. Lett. 118, 260602 (2017)

A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by ... [click to read more]

exact numerics on the transverse field Ising model, and demonstrate universality by adding non-integrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.

Scaling Theory of Entanglement at the Many-Body Localization Transition

Philipp T. Dumitrescu, Romain Vasseur, Andrew C. Potter

Phys. Rev. Lett. 119, 110604 (2017)

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the ... [click to read more]

correlation length, the average entanglement follows a sub-thermal volume law, whose coefficient is a universal scaling function. Furthermore, the full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume-law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump across the transition from fully thermal volume-law on the thermal side, to a pure area-law on the MBL side.

Quantum Channel Construction with Circuit Quantum Electrodynamics

Chao Shen, Kyungjoo Noh, Victor V. Albert, Stefan Krastanov, Michel H. Devoret, Robert J. Schoelkopf, S. M. Girvin, Liang Jiang

Phys. Rev. B 95, 134501 (2017)

Quantum channels can describe all transformations allowed by quantum mechanics. We provide an explicit universal protocol to construct all possible quantum channels, using a single qubit ancilla with quantum non-demolition readout and adaptive control. Our construction is efficient in both physical resources and circuit depth, and can be demonstrated using ... [click to read more]

superconducting circuits and various other physical platforms. There are many applications of quantum channel construction, including system stabilization and quantum error correction, Markovian and exotic channel simulation, implementation of generalized quantum measurements and more general quantum instruments. Efficient construction of arbitrary quantum channels opens up exciting new possibilities for quantum control, quantum sensing and information processing tasks.

Eigenstate phase transitions and the emergence of universal dynamics in highly excited states

S. A. Parameswaran, Andrew C. Potter, Romain Vasseur

Annalen der Physik , 1600302 (2017)

We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many-body localized (MBL) phases, and between MBL and thermal ... [click to read more]


Universal crossover from ground state to excited-state quantum criticality

Byungmin Kang, Andrew C. Potter, Romain Vasseur

Phys. Rev. B 95, 024205 (2017)

We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this system belong to different universality classes, characterized by infinite-randomness quantum critical behavior. Using strong-disorder renormalization group ... [click to read more]

techniques, we show that the crossover between the zero and finite energy density regimes is universal. We analytically derive a flow equation describing the unitary dynamics of this isolated system at finite energy density from which we obtain universal scaling functions along the crossover.

Quantum preparation uncertainty and lack of information

Filip Rozpędek, Jędrzej Kaniewski, Patrick J. Coles, Stephanie Wehner

New J. Phys. 19 023038 (2017)

The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we ... [click to read more]

critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. We answer this question affirmatively by showing that for the well known measurements employed in BB84 quantum key distribution, the amount of uncertainty can indeed be related to the amount of available information about additional registers determining the choice of the measurement. We proceed to show that also for other measurements the amount of uncertainty is in part connected to a LOI. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states.

Symmetry constraints on many-body localization

Andrew C. Potter, Romain Vasseur

Phys. Rev. B 94, 224206 (2016)

We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g. all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible ... [click to read more]

alternative fates of non-equilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry enriched topological orders.

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

Romain Vasseur, Joel E. Moore

J. Stat. Mech. (2016) 064010

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis ... [click to read more]

is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.

Particle-hole symmetry, many-body localization, and topological edge modes

Romain Vasseur, Aaron J. Friedman, S. A. Parameswaran, Andrew C. Potter

Phys. Rev. B 93, 134207 (2016)

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions ... [click to read more]

are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.

Expansion potentials for exact far-from-equilibrium spreading of particles and energy

Romain Vasseur, Christoph Karrasch, Joel E. Moore

Phys. Rev. Lett. 115, 267201 (2015)

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with ... [click to read more]

nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call ``expansion potentials'', expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies non-equilibrium Maxwell relations for the Drude weights. We verify our results via DMRG calculations for the XXZ chain.

Multifractal Orthogonality Catastrophe in 1D Random Quantum Critical Points

Romain Vasseur, Joel E. Moore

Phys. Rev. B 92, 054203 (2015)

We study the response of random singlet quantum critical points to local perturbations. Despite being insulating, these systems are dramatically affected by a local cut in the system, so that the overlap $G=\left|\langle \Psi_B |\Psi_A \rangle\right|$ of the groundstate wave functions with and without a cut vanishes algebraically in the ... [click to read more]

thermodynamic limit. We analyze this Anderson orthogonality catastrophe in detail using a real-space renormalization group approach. We show that both the typical value of the overlap G and the disorder average of $G^\alpha$ with $\alpha>0$ decay as power-laws of the system size. In particular, the disorder average of $G^\alpha$ shows a "multifractal" behavior, with a non-trivial limit $\alpha \to \infty$ that is dominated by rare events. We also discuss the case of more generic local perturbations and generalize these results to local quantum quenches.

Logarithmic Correlations in Quantum Hall Plateau Transitions

Romain Vasseur

Phys. Rev. B 92, 014205 (2015)

The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical origin of these logarithmic correlation functions remain however mysterious. Using the replica trick and the underlying symmetries of ... [click to read more]

these quantum critical points, we show here how to construct non-perturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the Integer quantum Hall plateau transition is also discussed.

Cavity State Manipulation Using Photon-Number Selective Phase Gates

Reinier W. Heeres, Brian Vlastakis, Eric Holland, Stefan Krastanov, Victor V. Albert, Luigi Frunzio, Liang Jiang, Robert J. Schoelkopf

Phys. Rev. Lett. 115, 137002 (2015)

The large available Hilbert space and high coherence of cavity resonators makes these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we ... [click to read more]

introduce the Selective Number-dependent Arbitrary Phase (SNAP) gate, which imparts a different phase to each Fock state component using an off-resonantly coupled qubit. We show that the SNAP gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the SNAP gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.

Holonomic quantum control with continuous variable systems

Victor V. Albert, Chi Shu, Stefan Krastanov, Chao Shen, Ren-Bao Liu, Zhen-Biao Yang, Robert J. Schoelkopf, Mazyar Mirrahimi, Michel H. Devoret, Liang Jiang

Phys. Rev. Lett. 116, 140502 (2016)

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between ... [click to read more]

that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems which support tunable nonlinearities, such as trapped ions and circuit QED.

Universal Control of an Oscillator with Dispersive Coupling to a Qubit

Stefan Krastanov, Victor V. Albert, Chao Shen, Chang-Ling Zou, Reinier W. Heeres, Brian Vlastakis, Robert J. Schoelkopf, Liang Jiang

Phys. Rev. A 92, 040303(R) (2015)

We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on number states of the oscillator, which together with displacement operations can achieve universal control of the oscillator. Based on our proof of universal control, ... [click to read more]

we provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, we present an efficient procedure to prepare the number state $\left|n\right\rangle$ using only $O\left(\sqrt{n}\right)$ operations. We also compare our scheme with known quantum control protocols for coupled qubit-oscillator systems. This universal control scheme of the oscillator can readily be implemented using superconducting circuits.

Universal properties of many-body delocalization transitions

Andrew C. Potter, Romain Vasseur, S. A. Parameswaran

Phys. Rev. X 5, 031033 (2015)

We study the dynamical melting of "hot" one-dimensional many-body localized systems. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for ... [click to read more]

such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics.

Exact overlaps in the Kondo problem

Sergei L. Lukyanov, Hubert Saleur, Jesper L. Jacobsen, Romain Vasseur

Phys. Rev. Lett. 114, 080601 (2015)

It is well known that the ground states of a Fermi liquid with and without a single Kondo impurity have an overlap which decays as a power law of the system size, expressing the Anderson orthogonality catastrophe. Ground states with two different values of the Kondo couplings have, however, a ... [click to read more]

finite overlap in the thermodynamic limit. This overlap, which plays an important role in quantum quenches for impurity systems, is a universal function of the ratio of the corresponding Kondo temperatures, which is not accessible using perturbation theory nor the Bethe ansatz. Using a strategy based on the integrable structure of the corresponding quantum field theory, we propose an exact formula for this overlap, which we check against extensive density matrix renormalization group calculations.

Quantum criticality of hot random spin chains

Romain Vasseur, Andrew C. Potter, S. A. Parameswaran

Phys. Rev. Lett. 114, 217201 (2015)

We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)$_k$ anyon chains that include the Ising and Potts chains as notable ... [click to read more]

examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses". We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $k\rightarrow\infty$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel non-equilibrium critical phases of matter.

Quantum revivals and many-body localization

R. Vasseur, S. A. Parameswaran, J. E. Moore

Phys. Rev. B 91, 140202 (2015)

We show that the magnetization of a single `qubit' spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstrate that the revival rate is strongly suppressed upon adding interactions after ... [click to read more]

a time scale corresponding to the onset of the dephasing that distinguishes many-body localized phases from Anderson insulators. In contrast, the ergodic phase acts as a bath for the qubit, with no revivals visible on the time scales studied. The suppression of quantum revivals of local observables provides a quantitative, experimentally observable alternative to entanglement growth as a measure of the `non-ergodic but dephasing' nature of many-body localized systems.

Universal nonequilibrium signatures of Majorana zero modes in quench dynamics

R. Vasseur, J. P. Dahlhaus, J. E. Moore

Phys. Rev. X 4, 041007 (2014)

The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of "quantum quench" to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically ... [click to read more]

decaying overlap (Loschmidt echo) ${\cal L}(t)=| < \psi(0) | \psi(t) > |^2\sim t^{-\alpha}$ for large times after the quench, with a universal critical exponent $\alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.

Edge Physics of the Quantum Spin Hall Insulator from a Quantum Dot Excited by Optical Absorption

Romain Vasseur, Joel E. Moore

Phys. Rev. Lett. 112, 146804 (2014)

The gapless edge modes of the Quantum Spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic ... [click to read more]

(Kondo) impurity, we consider a setup where the helical liquid is tunnel-coupled to a semiconductor quantum dot which is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the Quantum Spin Hall edge.

Operator content of the critical Potts model in d dimensions and logarithmic correlations

Romain Vasseur, Jesper Lykke Jacobsen

Nucl. Phys. B 880, 435--475 (2014)

Using the symmetric group $S_Q$ symmetry of the $Q$-state Potts model, we classify the (scalar) operator content of its underlying field theory in arbitrary dimension. In addition to the usual identity, energy and magnetization operators, we find fields that generalize the $N$-cluster operators well-known in two dimensions, together with their ... [click to read more]

subleading counterparts. We give the explicit form of all these operators -- up to non-universal constants -- both on the lattice and in the continuum limit for the Landau theory. We compute exactly their two- and three-point correlation functions on an arbitrary graph in terms of simple probabilities, and give the general form of these correlation functions in the continuum limit at the critical point. Specializing to integer values of the parameter $Q$, we argue that the analytic continuation of the $S_Q$ symmetry yields logarithmic correlations at the critical point in arbitrary dimension, thus implying a mixing of some scaling fields by the scale transformation generator. All these logarithmic correlation functions are given a clear geometrical meaning, which can be checked in numerical simulations. Several physical examples are discussed, including bond percolation, spanning trees and forests, resistor networks and the Ising model. We also briefly address the generalization of our approach to the $O(n)$ model.

Universal entanglement crossover of coupled quantum wires

Romain Vasseur, Jesper Lykke Jacobsen, Hubert Saleur

Phys. Rev. Lett. 112, 106601 (2014)

We consider the entanglement between two one-dimensional quantum wires (Luttinger Liquids) coupled by tunneling through a quantum impurity. The physics of the system involves a crossover between weak and strong coupling regimes characterized by an energy scale $T_B$, and methods of conformal field theory therefore cannot be applied. The evolution ... [click to read more]

of the entanglement in this crossover has led to many numerical studies, but has remained little understood, analytically or even qualitatively. We argue in this Letter that the correct universal scaling form of the entanglement entropy $S$ (for an arbitrary interval of length $L$ containing the impurity) is $\partial S/\partial \ln L = f(L T_B)$. In the special case where the coupling to the impurity can be refermionized, we show how the universal function $f(L T_B)$ can be obtained analytically using recent results on form factors of twist fields and a defect massless-scattering formalism. Our results are carefully checked against numerical simulations.

Apar-T: code, validation, and physical interpretation of particle-in-cell results

Mickaël Melzani, Christophe Winisdoerffer, Rolf Walder, Doris Folini, Jean M. Favre, Stefan Krastanov, Peter Messmer

A&A 558, A133, october 2013

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and ... [click to read more]

of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda.

Entanglement in quantum impurity problems is non perturbative

Hubert Saleur, Peter Schmitteckert, Romain Vasseur

Phys. Rev. B 88, 085413 (2013)

We study the entanglement entropy of a region of length 2L with the remainder of an infinite one dimensional gapless quantum system in the case where the region is centered on a quantum impurity. The coupling to this impurity is not scale invariant, and the physics involves a crossover between ... [click to read more]

weak and strong coupling regimes. While the impurity contribution to the entanglement has been computed numerically in the past, little is known analytically about it, since in particular the methods of conformal invariance cannot be applied because of the presence of a crossover length. We show in this paper that the small coupling expansion of the entanglement entropy in this problem is quite generally plagued by strong infrared divergences, implying a non-perturbative dependence on the coupling. The large coupling expansion turns out to be better behaved, thanks to powerful results from the boundary CFT formulation and, in some cases, the underlying integrability of the problem. However, it is clear that this expansion does not capture well the crossover physics. In the integrable case -- which includes problems such as an XXZ chain with a modified link, the interacting resonant level model or the anisotropic Kondo model -- a non perturbative approach is in principle possible using form-factors. We adapt in this paper the ideas of [1,2] to the gapless case and show that, in the rather simple case of the resonant level model, and after some additional renormalizations, the form factors approach yields remarkably accurate results for the entanglement all the way from short to large distances. This is confirmed by detailed comparison with numerical simulations. Both our form factor and numerical results are compatible with a non-perturbative form at short distance.

Crossover physics in the non-equilibrium dynamics of quenched quantum impurity systems

Romain Vasseur, Kien Trinh, Stephan Haas, Hubert Saleur

Phys. Rev. Lett. 110, 240601 (2013)

A general framework is proposed to tackle analytically local quantum quenches in integrable impurity systems, combining a mapping onto a boundary problem with the form factor approach to boundary-condition-changing operators introduced in Phys. Rev. Lett. 80, 4370 (1998). We discuss how to compute exactly two central quantities of interest: the ... [click to read more]

Loschmidt echo and the distribution of the work done during the quantum quench. Our results display an interesting crossover physics characterized by the energy scale T_b of the impurity corresponding to the Kondo temperature. We discuss in detail the non-interacting case as a paradigm and benchmark for more complicated integrable impurity models, and check our results using numerical methods.

A physical approach to the classification of indecomposable Virasoro representations from the blob algebra

Azat M. Gainutdinov, Jesper Lykke Jacobsen, Hubert Saleur, Romain Vasseur

Nuclear Physics B 873 (3), 614--681 (2013)

In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations corresponding to these quantum field theories remain dauntingly complicated, thus hindering our understanding of various critical ... [click to read more]

phenomena. We extend in this paper the construction of Read and Saleur (2007), and uncover a deep relationship between the Virasoro algebra and a finite-dimensional algebra characterizing the properties of two-dimensional statistical models, the so-called blob algebra (a proper extension of the Temperley--Lieb algebra). This allows us to explore vast classes of Virasoro representations (projective, tilting, generalized staggered modules, etc.), and to conjecture a classification of all possible indecomposable Virasoro modules (with, in particular, L_0 Jordan cells of arbitrary rank) that may appear in a consistent physical Logarithmic CFT where Virasoro is the maximal local chiral algebra. As by-products, we solve and analyze algebraically quantum-group symmetric XXZ spin chains and sl(2|1) supersymmetric spin chains with extra spins at the boundary, together with the "mirror" spin chain introduced by Martin and Woodcock (2004).

Phase Diagram of Ferroelastic Systems in the Presence of Disorder: Analytical Model and Experimental Verification

R. Vasseur, D. Xue, Y. Zhou, W. Ettoumi, X. Ding, X. Ren, T. Lookman

Phys. Rev. B 86, 184103 (2012)

There is little consensus on the nature of the glass state and its relationship to other strain states in ferroelastic materials which show the shape memory effect and superelasticity. We provide a thermodynamic interpretation of the known strain states, including precursory tweed and strain glass, by mapping the problem onto ... [click to read more]

a spin model and analytically obtaining the phase diagram using real-space renormalization group methods. We further predict a spontaneous transition from the glass state to the ordered martensite phase. We verify this prediction by mapping out the experimental phase diagram for the ternary ferroelastic alloy Ti$_{50}$(Pd$_{50-x}$Cr$_x$) and demonstrate the emergence of the spontaneous transition. Our work thus provides a consistent framework to understand the various experimental and theoretical studies on the glassy behavior associated with ferroelastic materials.

Logarithmic observables in critical percolation

Romain Vasseur, Jesper Lykke Jacobsen, Hubert Saleur

J. Stat. Mech. L07001 (2012)

Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing ... [click to read more]

the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.

Lattice fusion rules and logarithmic operator product expansions

A. M. Gainutdinov, R. Vasseur

Nucl. Phys. B 868, 223-270 (2013)

The interest in Logarithmic Conformal Field Theories (LCFTs) has been growing over the last few years thanks to recent developments coming from various approaches. A particularly fruitful point of view consists in considering lattice models as regularizations for such quantum field theories. The indecomposability then encountered in the representation theory ... [click to read more]

of the corresponding finite-dimensional associative algebras exactly mimics the Virasoro indecomposable modules expected to arise in the continuum limit. In this paper, we study in detail the so-called Temperley-Lieb (TL) fusion functor introduced in physics by Read and Saleur [Nucl. Phys. B 777, 316 (2007)]. Using quantum group results, we provide rigorous calculations of the fusion of various TL modules. Our results are illustrated by many explicit examples relevant for physics. We discuss how indecomposability arises in the "lattice" fusion and compare the mechanisms involved with similar observations in the corresponding field theory. We also discuss the physical meaning of our lattice fusion rules in terms of indecomposable operator-product expansions of quantum fields.

Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model

Romain Vasseur, Jesper Lykke Jacobsen

J. Phys. A 45, 165001 (2012)

The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be ... [click to read more]

promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the Kac form h_{r,s}, with integer indices r,s that we determine exactly both in the bulk and in the boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.

The puzzle of bulk conformal field theories at central charge c=0

Romain Vasseur, Azat M. Gainutdinov, Jesper Lykke Jacobsen, Hubert Saleur

Phys. Rev. Lett. 108, 161602 (2012)

Non-trivial critical models in 2D with central charge c=0 are described by Logarithmic Conformal Field Theories (LCFTs), and exhibit in particular mixing of the stress-energy tensor with a "logarithmic" partner under a conformal transformation. This mixing is quantified by a parameter (usually denoted b), introduced in [V. Gurarie, Nucl. Phys. ... [click to read more]

B 546, 765 (1999)], and which was first thought to play the role of an "effective" central charge. The value of b has been determined over the last few years for the boundary versions of these models: $b_{\rm perco}=-5/8$ for percolation and $b_{\rm poly} = 5/6$ for dilute polymers. Meanwhile, the existence and value of $b$ for the bulk theory has remained an open problem. Using lattice regularization techniques we provide here an "experimental study" of this question. We show that, while the chiral stress tensor has indeed a single logarithmic partner in the chiral sector of the theory, the value of b is not the expected one: instead, b=-5 for both theories. We suggest a theoretical explanation of this result using operator product expansions and Coulomb gas arguments, and discuss the physical consequences on correlation functions. Our results imply that the relation between bulk LCFTs of physical interest and their boundary counterparts is considerably more involved than in the non-logarithmic case.

Indecomposability parameters in chiral Logarithmic Conformal Field Theory

Romain Vasseur, Jesper Lykke Jacobsen, Hubert Saleur


Work of the last few years has shown that the key algebraic features of Logarithmic Conformal Field Theories (LCFTs) are already present in some finite lattice systems (such as the XXZ spin-1/2 chain) before the continuum limit is taken. This has provided a very convenient way to analyze the structure ... [click to read more]

of indecomposable Virasoro modules and to obtain fusion rules for a variety of models such as (boundary) percolation etc. LCFTs allow for additional quantum numbers describing the fine structure of the indecomposable modules, and generalizing the `b-number' introduced initially by Gurarie for the c=0 case. The determination of these indecomposability parameters has given rise to a lot of algebraic work, but their physical meaning has remained somewhat elusive. In a recent paper, a way to measure b for boundary percolation and polymers was proposed. We generalize this work here by devising a general strategy to compute matrix elements of Virasoro generators from the numerical analysis of lattice models and their continuum limit. The method is applied to XXZ spin-1/2 and spin-1 chains with open (free) boundary conditions. They are related to gl(n+m|m) and osp(n+2m|2m)-invariant superspin chains and to nonlinear sigma models with supercoset target spaces. These models can also be formulated in terms of dense and dilute loop gas. We check the method in many cases where the results were already known analytically. Furthermore, we also confront our findings with a construction generalizing Gurarie's, where logarithms emerge naturally in operator product expansions to compensate for apparently divergent terms. This argument actually allows us to compute indecomposability parameters in any logarithmic theory. A central result of our study is the construction of a Kac table for the indecomposability parameters of the logarithmic minimal models LM(1,p) and LM(p,p+1).

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis

Romain Vasseur, Turab Lookman, Subodh R. Shenoy

Phys. Rev. B 82, 094118 (2010)

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local meanfield approximation of their pseudospin hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their $N_{OP}$-component order parameters, with Landau free energies that have a single ... [click to read more]

zero-strain 'austenite' minimum at high temperatures, and spontaneous-strain 'martensite' minima of $N_V$ structural variants at low temperatures. In a reduced description, the strains at Landau minima induce temperature-dependent, clock-like $\mathbb{Z}_{N_V +1}$ hamiltonians, with $N_{OP}$-component strain-pseudospin vectors ${\vec S}$ pointing to $N_V + 1$ discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local meanfield approximation of their pseudospin hamiltonians, that include the powerlaw interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in a generalized Blume-Capel model. We then consider transitions with two-component ($N_{OP} = 2$) pseudospins: the equilateral to centred-rectangle ($N_V =3$); the square to oblique polygon ($N_V =4$); the triangle to oblique ($N_V =6$) transitions; and finally the 3D cubic to tetragonal transition ($ N_V =3$). The local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related hamiltonians illustrate that structural-transitions in materials science can be the source of interesting spin models in statistical mechanics.