Lectures by Jamie Sikora and Antonios Varvitsiotis at the Centre for Quantum Technologies, National University of Singapore

The goal of this course is to give a thorough introduction to semidefinite programming and to examine its use in the study of problems arising in quantum information and computation

Where: S15-06-22

When: Tuesdays (10am - 12pm) and Thursdays (10am - 11am)

Final Grade

70% Assignments, 30% Class Project (20% Report, 10% Presentation)

Related literature

Lecture Notes by John Watrous

Convex Optimization by Stephen Boyd and Lieven Vandenberghe

Lectures on Modern Convex Optimization by Aharon Ben-Tal and Arkadi Nemirovski

Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang

Assignments

Assignment 1: Semidefinite Programming and Quantum Computing

Assignment 2: Quantum Complexity Theory

Assignment 3: Quantum Cryptography

Assignment 4: Quantum Nonlocal Games

Lectures and lecture notes

Lecture 01: Informal Introduction to Quantum Mechanics

Lecture 02: Informal Introduction to Semidefinite Programming

Lecture 03: Mathematical Preliminaries

Lecture 04: Introduction to Quantum Information I

Lecture 05: Introduction to Quantum Information II

Lecture 06: Introduction to Quantum Information III

Lecture 07: Semidefinite Programming I

Lecture 08: Semidefinite Programming II

Lecture 09: Semidefinite Programming III

Lecture 10: Quantum State Discrimination

Lecture 11: SDPs for the Quantum Fidelity Function

Lecture 12: Uhlmann's Theorem and Alberti's Theorem are Dual

Lecture 13: The Ellipsoid Algorithm for Solving SDPs

Lecture 14: Quantum Complexity Theory and an SDP for QMA

Lecture 15: An Exponential Time Algorithm for QMA

Lecture 16: Perfect Parallel Repetition for QMA

Lecture 17: Quantum Interactive Proofs and an SDP for QIP

Lectures 18+19: QIP = PSPACE (guest lectures by Sarvagya Upadhyay)

Lecture 20: Perfect Parallel Repetition for QIP

Lecture 21: Quantum Bit-Commitment Introduction

Lecture 22: SDPs and Optimal Bounds for Two-Round Quantum Bit-Commitment

Lecture 23: Quantum Coin-Flipping Introduction

Lecture 24: Quantum Coin-Flipping Based on EPR Sharing

Lecture 25: Kitaev's Lower Bound for Quantum Coin-Flipping

Lecture 26: Optimal Quantum Protocols for Weak and Strong Coin-Flipping

Lecture 27: Nonlocal Games

Lecture 28: Two-Player XOR Games

Lecture 29: The CHSH Game

Lectures 30+31+32: Perfect Parallel Repetition of Quantum XOR Games