# Past Independent Study Projects

We have a number of spots open for independent study projects at the BS and MS level you can peruse. Here we list successful past projects.

## Waveguide-Cavity interactions for quantum information | 2022

*By:* Matias Bundgaard-Nielsen | Technical University of Denmark student collaborating with MIT

Many networking tasks in quantum information are realized by having a photon as a long range carrier of quantum information. Modeling the interaction of such a photon with a local node can be difficult if we are to capture the entirety of the analog quantum dynamics. This project builds a number of related simulation techniques and algorithms, in particular focused on being able to model aritrary wave-packet profiles.

*Results:*

`CavityWaiveguide.jl`

prototype of a library extending`QuantumOptics.jl`

.

## Expander graphs and Cayley complexes for Quantum LDPC codes | 2022

*By:* Vaishnavi Addala | MIT Undergraduate

Error correcting codes are a group of techniques that permit encoding information in a protected redundant fashion, thus enabling reconstructing damaged records. Error correcting codes are usually represented as a set of linear equations that are fulfilled by the physical bits. These linear constraints can be generated in a variety of ways – particularly good codes have been generated by using expander graphs as a guide to which qubits to be "connected" by a constraint. This project endeavors to generate many such classes of expander graphs and LDPC error correcting codes.

*Results:*

Contributions to the

`QuantumExpanders.jl`

library of expander graph generators and LDPC codes.

## Optimization of entanglement purification circuits | 2022

*By:* Vaishnavi Addala | MIT Undergraduate

We then use our fast Bell circuit simulator together with a simple discrete optimization algorithm to design purification circuits from $n$ raw Bell pairs to $k$ purified pairs and study their application to the teleportation of logical qubits in second generation quantum repeaters. The resulting purification circuits are the best known purification circuits for 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 the teleportation is greatly increased.

*Results:*

`Qevo.jl`

library implementing the circuit optimizer.Upcoming "Faster Bell Simulations and Full-stack Optimization of Entanglement Purification" paper.

## GPU accelerated simulator for Clifford circuits | 2021

*By:* Shu Ge | MIT Undergraduate

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 distillation and error correction circuits that function well, especially on today's imperfect hardware, is an open question. 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.

*Results:*

`BPGates.jl`

library implementing the faster simulation algorithm.Upcoming "Faster Bell Simulations and Full-stack Optimization of Entanglement Purification" paper.

## All-Photonic Artificial Neural Network Processor Via Non-linear Optics | 2020

*By:* Jasvith Raj Basani | Birla Institute of Technology and Science Undergraduate collaborating with MIT

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 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.

*Results:*

The paper "All-Photonic Artificial Neural Network Processor Via Non-linear Optics" and related patent.

## GPU accelerated simulator for Clifford circuits | 2022

*By:* Torque Dandachi | MIT Undergraduate

Simulation of Clifford circuits involves significant amounts of linear algebra with boolean matrices. This enables the use of many standard computation accelerators like GPUs, as long as these accelerators support bit-wise operations. The main complications is that the elements of the matrices under consideration are usually packed in order to increase performance and lower memory usage, i.e. a vector of 64 elements would be stored as a single 64 bit integer instead of as an array of 64 bools. This project consists of implement the aforementioned linear algebra operations in GPU kernels, and then seamlessly integrating them in the rest of the QuantumClifford library.

*Results:*

In-depth evaluation of different GPU implementation strategies. Full implementation was not finished.

`QuantumCliffordCUDA.jl`

library with an initial implementation.

## Optimal Control of Unresolved Defect Centers | 2020

*By:* Torque Dandachi | MIT Undergraduate

A central goal in many quantum information processing applications is a network of quantum memories that can be entangled with each other while being individually controlled and measured with high fidelity. This goal has motivated the development of programmable photonic integrated circuits (PICs) with integrated spin-based quantum memories in diamond color center spin-photon interfaces. However, this approach introduces a challenge in the microwave (MW) control of individual spins within closely packed registers. That challenge can be overcome by selective manipulation of individual spin qubits addressed via tunable magnetic field gradients and simultaneous optimal quantum control of multiple qubits using numerically optimized MW pulse shaping. The combination of highly localized optical control together with selective spin manipulation by optimal quantum control methods opens the path to scalable quantum networks on intra-chip and inter-chip platforms.

*Results:*

The entirety of the optimal control code used in "Multiplexed control of spin quantum memories in a scalable photonic circuit".

`git`

repository with the control pulse optimizer.