COMPSCI 490Q: Quantum Information Science - Spring of 2023

Quantum information science (QIS) revolutionizes our understanding of the fundamental laws of the universe and promises world-altering improvements in a number of practical computational tasks. For theoretical computer scientists, QIS provides the means to unlock the ultimate computational powers available to us in this universe. For programmers and computer engineers, QIS offers the tools to run simulations and optimizations otherwise infeasible on classical computers. For theoretical physicists, QIS gives us hope of resolving paradoxes foundational to our understanding of Nature. And for experimentalists and engineers, QIS also enables the creation of exquisite sensors and novel communication tools, far outperforming what is classically permitted.

This class will introduce the notion of quantum probability amplitudes, i.e., the "correct" probabilistic description of Nature, and describe how these quantum phenomena permit the creation of new types of computational machines. The introduction to foundational quantum information science will be followed by a few practical (and impractical) quantum algorithms, illustrating the counterintuitive computational powers of quantum mechanics. The latter half of the class will focus on the difficulties of creating such extremely fragile computational machines in our noisy and unforgiving real world.

Spring2023     InstructorProf. Stefan Krastanov
LocationFlint Lab 103     skrastanov@umass.edu
TimeMW 11:15-12:30     LGRC A211F
     Prof. Office Hours signup Mon before/after class
     TAAmir Reza Ramtin
     aramtin@umass.edu
     TA Office Hours Fri 13:00-15:00 in LGRT T223

Website at lab.krastanov.org/undergrad-qis.

Online course management through Moodle.

Prerequisites

A grade of C or better in each of:

  • MATH 132 Calculus II

  • MATH 235 Introduction to Linear Algebra

  • one of COMPSCI 240 or STAT 515 or PHYSICS 281 or PHYSICS 287

These classes could be helpful but are not necessary:

  • MATH 233 Multivariate Calculus

  • COMPSCI 250 Introduction to Computations

  • COMPSCI 311 Introduction to Algorithms

Learning Objectives

  1. Understanding of classification of deterministic, probabilistic, and quantum algorithms, in particular the difference between classical probability and quantum probability amplitude;

  2. Familiarity with the "killer apps" for quantum computing and networking hardware, where they have capabilities beyond those of classical computers;

  3. Understanding of the limitations of quantum computers: in what situations are they not more powerful than classical computers;

  4. Modeling of noisy quantum hardware and standard error correction techniques permitting the creation of reliable quantum hardware out of noisy unreliable quantum systems.

Content

ClassTopicConcepts
1,2Classical Probability TheoryBayesian vs Frequentist, parametrization of ignorance, stochastic matrices, probability in physics, probability in computation
3,4Quantum Probability AmplitudesClassical vs quantum correlation, Unitary matrices, Particles or waves, Observer effect, Delayed choice experiment, Bomb defusing
5,6EntanglementClassical vs quantum correlation, Bell's game and Bell's inequality
7Quantum Key DistributionIndistinguishability of eavesdropper and noise
8TeleportationState teleportation, gate teleportation, ultradense coding
9,10Quantum AlgorithmsAlgorithms of Deutsch–Jozsa, Bernstein–Vazirani, Simon, Shor, Fourier Transform, Phase Estimation
11,12Quantum AlgorithmsGrover's search, Quantum Random Walks
13,14Quantum AlgorithmsChemistry simulations, optimizations
15Quantum AlgorithmsLinear Algebra, Machine Learning
16Noisy EntanglementEntanglement purification and distillation
17,18,19Noisy Quantum MemoriesError correction, Linear Binary Codes, Stabilizer Codes, Syndrome measurement, Syndrome decoding, Repetition code, CSS code, Toric code, LDPC code
20,21,22Noisy Quantum ComputationFault tolerance, Fault tolerant syndrome measurement, Transversal gates, Magic states
23,24Efficient classical simulationsStabilizer states, Clifford circuits

Textbooks

A variety of materials will be provided as the class progresses and each lecture will have suggested readings from multiple sources. You can see a preview of the most important sources.

Exercises

There are optional ungraded exercises you can use to practice. Office hours would be a good place to discuss them.

Calendar

26 class days

Exams:

  • 1st Midterm, take home exam, 7am-11:59pm, Tue, March 7th

  • 2nd Midterm, take home exam, 7am-11:59pm, Thu, April, 13th

  • Final, in-person written exam, date TBD

Take home exams are completely open book and open internet, but no communication with other sentient beings is permitted (e.g., yes to using search engines, no to asking new questions on forums, no to working with classmates).

The final exam is open book, but you can bring only non-electronic resources (e.g., books and notes, but for best results rely on your own notes).

Homeworks:

Due on Friday of the same week they were given. Given on:

  • Feb 27th

  • Mar 20th

  • Apr 3rd

  • May 1st

Extra credit or ungraded homeworks might be considered.

Collaboration is encouraged for the homeworks (and should be disclosed), but the final solutions have to be your own and copying of others' work is forbidden.

WeekContent
Feb 62 lectures
Feb 13lectures canceled due to conference, to be rescheduled later in the year
Feb 201 lecture, Presidents' Day Mon Holiday, Wed schedule change
Feb 272 lectures
Mar 62 lectures
Mar 13Spring Recess
Mar 202 lectures
Mar 272 lectures
Apr 32 lectures
Apr 102 lectures
Apr 171 lecture, Patriot's Day Mon/Tue Holiday
Apr 242 lectures
May 12 lectures
May 82 lectures
May 152 lectures, Wed last day of classes

Topics not covered

These are important topics we will not have the time to cover, but you might want to pursue in the future for fuller understanding of the field. Feel free to also discuss them during office hours.

  • Analog quantum dynamics: Hamiltonians, Schroedinger's equation

  • Noisy quantum dynamics: Kraus operators, Lindblad Master Equation, Quantum Trajectories, CPTP maps

  • Hardware realizations: Transmons and microwave cavities, trapped ions, color centers, photonics

  • Continuous variable quantum information, Bosonic codes, Gaussian quantum information

  • Supremacy experiments, sampling

  • Quantum chemistry simulations

  • Adiabatic quantum computation

  • Quantum optimization algorithms

  • Quantum machine learning

  • Cluster state computation, One-way quantum computers

  • Compilation of quantum circuits

  • Quantum sensors

  • Applications to Fundamental Physics, Cosmology, High Energy Physics, Black holes

Grading

A 3 credit undergrad class graded as Letter grade or Optional Student Grading. Letter grades are A, A-, B+, B, B-, C+, C, C-, D+, D, F.

  • 10% before-class short quizzes (graded complete-A / incomplete-F)

  • 40% homeworks (letter graded, counting only the 3 best homeworks, discarding the grade from the worst one)

  • 30% midterms (letter graded)

  • 20% final (letter graded)

Homework late return policy: each day the homework is late, the grade for that particular homework is lowered by a factor of 0.7, compounding.

Use of Tools (solvers, textbooks, AI, etc) during exams and for homework

As long as you disclose the use, you can use any personal tool you can think of to help with take-home exams and homework. That includes:

  • textbooks

  • search engines

  • numerical or symbolic software

  • AI language models and chat tools (e.g. ChatGPT)

However you have to disclose that you used such a tool. In particular, if you find a creative use of such a tool, you might be asked to demonstrate to the class the new technique you have discovered.

Beware, AI language models like ChatGPT might very often produce absolute garbage nonsense while presenting it with a veneer of authority and certainty.

For the final exam you are permitted only non-electronic tools. You can bring a hundred kilograms of books if you want, but you would probably obtain better results if you prepare your own summary notes.

You are not permitted to copy the work of another sentient being for any exam or homework.

Academic Honesty Statement

Copying of written homeworks, or exams or "teamwork" on an assignment (unless teaming is explicitly part of that assignment) is not permitted. You can talk to other students about the assignments, and ask/answer questions - it is great to learn from each other - but the work you hand in must be your own. A student found copying the work of others will receive a grade of F for the course. If you are having trouble with an assignment or if you are having trouble meeting a deadline, see the instructor or the TA; we will bend over backwards to help you but we will not tolerate cheating. Please read the UMass Academic Code of Conduct Policy.

Accommodation Statement

The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students. If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements. For further information, please visit Disability Services.

CC BY-SA 4.0 Stefan Krastanov. Last modified: February 15, 2024. Website built with Franklin.jl and the Julia programming language.