Mathematics Of Quantum Computing: An Introduction

Description

This textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix of solutions. Front Matter ....Pages i-xix Introduction (Wolfgang Scherer)....Pages 1-9 Basic Notions of Quantum Mechanics (Wolfgang Scherer)....Pages 11-75 Tensor Products and Composite Systems (Wolfgang Scherer)....Pages 77-125 Entanglement (Wolfgang Scherer)....Pages 127-160 Quantum Gates and Circuits for Elementary Calculations (Wolfgang Scherer)....Pages 161-246 On the Use of Entanglement (Wolfgang Scherer)....Pages 247-341 Error Correction (Wolfgang Scherer)....Pages 343-402 Adiabatic Quantum Computing (Wolfgang Scherer)....Pages 403-497 Epilogue (Wolfgang Scherer)....Pages 499-500 Back Matter ....Pages 501-764