Quantum Information and Computation

Lecturer: Richard Jozsa
Lent Term 2018, 24 lectures, Monday, Wednesday, Friday at 11am in MR3

COURSE DESCRIPTION:

Quantum processes can provide extraordinary benefits for information processing, communication and security, offering striking novel features beyond the possibilities of standard (classical) paradigms. These include (i) remarkable new kinds of algorithms (so-called quantum algorithms) providing an exponentially faster method for some computational tasks, (ii) new modes of communication such as quantum teleportation, and (iii) the possibility of unconditionally secure communication in quantum cryptography. Most of these exciting developments have occurred in just the past few decades and they underpin transformative applications for quantum technologies that are currently being developed.

This course will provide an introduction to these topics. No previous contact with the theory of computation or information will be assumed. 1B Quantum Mechanics is essential, but only in so far as to provide prior exposure to basic ideas of quantum mechanics. This course will rest on quantum theory just in a finite dimensional setting, so the principal mathematical ingredients (from finite dimensional linear algebra) will be readily accessible. We will begin by expounding the principles of quantum mechanics in our setting (and Dirac notation) and then immediately make connections to information (quantum states viewed as information carriers, quantum teleportation) and computation (notion of qubits and quantum gates). Then we will discuss quantum cryptography (quantum key distribution), and quantum computing, culminating in an exposition of principal quantum algorithms, including the Deutsch-Jozsa algorithm, Grover's searching algorithm and an overview of Shor's quantum factoring algorithm.

The course is richly cross-disciplinary in its conceptual ingredients and its novel perspective is also finding wide application in modern theoretical physics. It will be of interest to pure and applied mathematicians alike.

COURSE MATERIALS:

All course materials for 2018 will be downloadable from links below (to be added as the term progresses).
Note for supervisors: solutions to exercise sheets are available on request from Richard Jozsa (rj310@cam.ac.uk)

UPDATES DIARY 2018:

January 23rd: Exercise Sheet 1 uploaded.
January 28th: Lecture notes for first half (approx) of course uploaded.
February 11th: Exercise Sheet 2 uploaded.
February 22nd: FULL lecture notes uploaded. This file extends the previous first half, which remains unchanged.
February 22nd: Exercise Sheet 3 uploaded.
March 4th: Exercise Sheet 4 uploaded.
March 10th: Guide to examinable material uploaded.
May 3rd: Sheet of Revision Questions uploaded. Thanks to M. Yoganathan, S. Strelchuk and S. Subramanian for help with inputs.

AttachmentSize
QIC LectNotesFirstHalf.pdf343.6 KB
QIC LectNotesFULL.pdf517.72 KB
QIC Exsheet1.pdf144.6 KB
QIC Exsheet2.pdf150.96 KB
QIC Exsheet3.pdf156.23 KB
QIC Exsheet4.pdf195.33 KB
QIC ExamGuide.pdf44.29 KB
QIC RevisionQns.pdf123.5 KB