Advanced Topics in Quantum Information Theory
Course Number: CSC 2429 HF/MAT 1752 HF
Zoom link:
https://utoronto.zoom.us/j/94134553829 (Passcode: on Quercus, or e-mail me)
Date/Time: Tuesday 4-6pm
First meeting: September 8.
Description
The goal of the course is to take a deep dive into some of the most exciting topics at the frontier of quantum complexity theory and quantum cryptography. There have been very exciting developments recently, including the connection between the complexity of quantum multiprover interactive proofs and questions in functional analysis and operator algebras; new cryptographic primitives such as quantum money/quantum copy-protection; quantum homomorphic encryption and the use of lattice cryptography; the quantum PCP Conjecture and its connections with condensed matter physics. This course will cover advanced and cutting edge topics in quantum information theory, organized into the following two themes:
Classical verification of quantum systems: nonlocal games, self-testing, verifiable delegation of quantum computation, the use of lattice cryptography, and MIP* = RE and its connection to the Connes’ Embedding Conjecture.
Hamiltonian complexity theory: QMA completeness, local Hamiltonians, QMA(2), Quantum PCP Conjecture, area laws, and algorithms for solving local Hamiltonians.
This is a theory-based course that assumes familiarity with quantum information, and familiarity with algorithms/complexity theory is strongly recommended. Students will be responsible for completing 3 problem sets, scribing lecture notes, and writing a final project report.
Final Project Showcase
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Quantum nonlocal games and approximate representation theory Deepanshu Kush, Adrian She |
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Entanglement vs Communication in Nonlocal Games Yuval Efron, Hugh Goatcher |
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Quantum Money Logan Murphy, Hao Zhang |
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Closed time-like curves and other models of hypercomputation Ariel Kelman, Dong Hao Ou Yang |
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Overparameterization in QAOA Wentao Cui, Stephen Zhang |
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1D Area Laws Juan Castaneda |
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Exponential Advantages in Quantum Machine Learning through Feature Mapping Andrew Nader, Kyle Oppenheimer, Gary Tom |
Scribe Notes
The complete set of scribe notes can be found here. Feedback/comments/typos/corrections are very welcome!
Problem Sets
- Problem set 1. Due September 25
- Problem set 2. Due October 30
Schedule
| Date | Topic, Notes, and References |
|---|---|
| September 8 | Administrativa. Quantum information refresher, Bell’s Theorem and the CHSH game. Scribe notes |
| September 15 | Finish up the CHSH game. Introduction to Hamiltonian Complexity. Scribe notes |
| September 22 | QMA and QMA-completeness of the local Hamiltonians problem. Scribe notes |
| September 29 | Finish up QMA-completeness. Classical PCP Theorem. Scribe notes |
| October 6 | Quantum PCP Conjecture. Scribe notes |
| October 13 | Complexity of quantum states, and no-go results for Quantum PCP. Scribe notes |
| October 20 | Rigidity of the CHSH game. Scribe notes |
| October 27 | Grilo’s two-prover protocol for verifying quantum computations. Scribe notes |
| November 3 | MIP* = RE, part I. Scribe notes |
| November 17 | MIP* = RE, part II Scribe notes |
| November 24 | MIP* = RE, part III. Scribe notes |
| December 1 | The power of unentanglement and QMA(2). Scribe notes |