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
  2. 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.
November 3 MIP* = RE, part I
November 17 MIP* = RE, part II
November 24 Verifying quantum computations using cryptography.
December 1 TBD.