CS 880 - Quantum Computing Spring 2020

Course Description

Remarkable results from the last three decades have given evidence that computers based on quantum mechanical principles could profoundly alter the nature of information processing. Efficient algorithms for breaking widely-used cryptographic systems, query efficient strategies for database searches, techniques like teleportation and superdense coding, and provably secure schemes for cryptographic key distribution have demonstrated how differently quantum information behaves, and how these properties can be exploited to solve certain computational tasks better than known classically.

This course focuses on the algorithmic aspects of quantum computing, its potential and its limitations. We develop a quantum model of computation, and discuss known paradigms of efficient quantum computation, including amplitude amplification, phase estimation, and quantum walks. We apply them to computational problems such as satisfiability, the hidden subgroup problem (including integer factoring and discrete log), clustering, sampling, solving systems of linear equations, and Hamiltonian simulation.

We also discuss communication and other interactive processes, including cryptographic ones such as key distribution, bit commitment, and zero-knowledge proofs. Time permitting and depending on the interests of the audience, we may cover additional topics such as error correction and fault tolerance.

Prerequisites

Knowledge of linear algebra at the level of Math 340, and familiarity with probability and algorithms is assumed. No specific knowledge of theoretical computer science is required; the necessary background will be provided. No knowledge of physics is needed.

Text

Scribe notes will be made available via Canvas. The notes from a prior offering as well as the lecture notes of a course by Ronald de Wolf are good references for large parts of the course.

Work

• Scribe notes. You will be expected to scribe notes in LaTeX for one or two lectures. Templates will be provided. Someone who missed a lecture should be able to learn the material from the scribe notes.

• Homework. There will be three problem sets. They are optional but strongly recommended if you want to become fluent in the course material.

• Project. There will be no exams. Instead, you are expected to work out a project on a topic related to the course material. Suggestions will be provided. You are also welcome to design a project of your own.

Lectures

TR 2:30-3:45pm in Psychology 121.

Instructor

Dieter van Melkebeek