Quantum computation and quantum information. A mathematical perspective
type: Item
instance of: scholarly article
title: Quantum computation and quantum information. A mathematical perspective
author: J. M. Landsberg
published in: Graduate Studies in Mathematics
publication date: 2024-06-13T00:00:00Z
review text: This book is for a one-semester course in quantum computing and quantum information theory, emphasizing the mathematical aspects and the historical continuity of both algorithms and information theory.\N\NThe synopsis of the book goes as follows.\N\N\begin{itemize}\N\item[Chapter 1] presents classical and probabilistic computation via linear algebra in order to pave the way for quantum computation.\N\N\item[Chapter 2] covers aspects of quantum mechanics needed for quantum computation.\N\N\item[Chapter 3] covers the basics of quantum computing and the standard quantum algorithms. It presents the algorithms of Grover and Simon, respectively in \S 3.1 and \S 3.2. Elementary number theory needed for the algorithms of Miller-Rabin and Shor is presented in \S 3.3. \S 3.4 presents the Miller-Rabin primality test. \S 3.5 discusses admissible quantum gates. \S 3.6 is concerned with Shor's algorithm.\N\N\item[Chapter 4] is concerned with classical information theory. \S 4.1 deals with toy examples leading up to the notion of channel capacity. \S 4.2 gives a preliminary version of Shannon's noiseless channel theorem. \S 4.3 studies entropy as a function on probability distributions with many interesting properties. \S 4.4 gives the statement and proof of Shannon's noiseless channel theorem, along with several variants. \S 4.5 establishes the noisy channel theorem.\N\N\item[Chapter 5] serves as preparation for the quantum information theory presented in Chapter 6. \S 5.1 presents a convenient reformulation of the postulates of quantum mechanics in terms of density operators, which gives rise to several new concepts and ways of viewing composite systems as discussed in \S 5.2. \S 5.3 discusses distances between density operators. \S 5.4 discusses briefly singular value and polar decompositions. \S 5.5 defines quantum channels, describing several presentations of them.\N\N\item[Chapter 6] is concerned with quantum information. \S 6.1 presents a quantum version of Shannon's noisel…
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 81P45
Mathematics Subject Classification ID: 81P68
Mathematics Subject Classification ID: 68Q12
Mathematics Subject Classification ID: 94A15
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 94A24
zbMATH DE Number: 7864918
MaRDI profile type: Publication
DOI: 10.1090/GSM/243
description: scientific article; zbMATH DE number 7864918