Quantum Information and Computation

Quantum Information and Computation(C)

QUANTUM INFORMATION AND COMPUTATION (C)
Part IB Quantum Mechanics is desirable.

Introduction

  • Why quantum information and computation. The basic idea of polynomial vs exponential computational complexity. [1]

Quantum mechanics and quantum information

  • Basic principles of quantum mechanics and Dirac notation in a finite-dimensional setting. Composite systems and tensor products, projective measurements. Two-dimensional systems: qubits and Pauli operations. Definition of an entangled state. [3]

Quantum states as information carriers

  • The no-cloning theorem. Optimal discrimination of non-orthogonal pure states; the Helstrom bound. Local quantum operations. The no-signalling theorem. [4]

Quantum teleportation and dense coding

  • Bell states and basic properties; quantum dense coding. Exposition of quantum teleportation. Consistency of quantum teleportation with the no-signalling and no-cloning theorems. [2]

Quantum cryptography

  • Cryptographic key distribution and the one-time pad. Quantum key distribution: the BB84 protocol. Sketch of the security of the BB84 protocol against individual attacks. *Brief discussion of implementations of quantum key.* [3]

Basic principles of quantum computing

  • Quantum logic gates and the circuit model of quantum computation. Universal gate sets. *Brief discussion of implementations of quantum computers*. Basic notions of quantum computational complexity. Informal definition of the complexity classes P, BPP and BQP. [3]

Basic quantum algorithms

  • Query complexity and promise problems. The Deutsch–Jozsa algorithm. The quantum Fourier transform. Quantum algorithm for periodicity finding. [4]

Grover’s quantum searching algorithm

  • Introduction to search problems and the complexity class NP. Exposition of Grover’s quantum searching algorithm. [2]

Shor’s quantum factoring algorithm

  • Exposition of Shor’s quantum factoring algorithm (proofs of classical number-theory ingredients not examinable). [2]

Appropriate books

  • M. Nielsen and I. Chuang Quantum Computation and Quantum Information. CUP 2000
  • B. Schumacher and M. Westmoreland Quantum Processes, Systems, and Information. CUP 2010
  • S. Loepp and W. Wootters Protecting Information: From Classical Error Correction to Quantum Cryptography. Academic Press 2006
  • J. Preskill Lecture Notes for Physics 229: Quantum Information and Computation, CreateSpace. Independent Publishing Platform (in press). Currently available at http://www.theory.caltech.edu/people/preskill/ph229/notes/book.ps

Associated GitHub Page

https://jaircambridge.github.io/Quantum-Informatiom-and-Computation-C/

Quantum Information and Computation

Lecturer: Richard Jozsa
Lent Term 2021, 24 lectures, Tuesay, Thursday, Saturday at 9am

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 provided course materials for Lent Term 2021 will be available on the Moodle page for this course.
(to be provided as the course progresses).
Recordings of all lectures will be available on the Moodle page too.