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.

Syllabus
Project guidelines

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.

Problem Sets

  1. Problem set 1. Due September 25

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 The Quantum PCP Conjecture