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1st Edition

Quantum Computation



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ISBN 9781032206486
February 23, 2023 Forthcoming by Chapman and Hall/CRC
400 Pages 122 B/W Illustrations

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Book Description

Quantum Computation presents the mathematics of quantum computation. The purpose is to introduce the topic of quantum computing to students in computer science, physics and mathematics who have no prior knowledge of this field.

The book is written in two parts. The primary mathematical topics required for an initial understanding of quantum computation are dealt with in Part I: sets, functions, complex numbers and other relevant mathematical structures from linear and abstract algebra. Topics are illustrated with examples focussing on the quantum computational aspects which will follow in more detail in Part II.

Part II discusses quantum information, quantum measurement and quantum algorithms. These topics provide foundations upon which more advanced topics may be approached with confidence.

Features:

  • A more accessible approach than most competitor texts, which move into advanced, research-level topics too quickly for today's students.
  • Part I is comprehensive in providing all necessary mathematical underpinning, particularly for those who need more opportunity to develop their mathematical competence.
  • More confident students may move directly to Part II and dip back into Part I as a reference.
  • Ideal for use as an introductory text for courses in quantum computing.
  • Fully worked examples illustrate the application of mathematical techniques.
  • Exercises throughout develop concepts and enhance understanding.
  • End-of-chapter exercises offer more practice in developing a secure foundation.

Table of Contents

Preface

Acknowledgements

Symbols

Part I Mathematical Foundations for Quantum Computation

1. Mathematical preliminaries

2. Functions and their application to digital gates

3. Complex numbers

4. Vectors

5. Matrices

6. Vector spaces

7. Eigenvalues and eigenvectors of a matrix

8. Group theory

9. Linear transformations

10. Tensor product spaces

11. Linear operators and their matrix representations

Part II Foundations of quantum-gate computation

12. Introduction to Part II

13. Axioms for quantum computation

14. Quantum measurement 1

15. Quantum information processing 1: the quantum emulation of familiar invertible digital gates

16. Unitary extensions of the gates notQ, FQ, TQ and PQ: more general quantum inputs

17. Quantum information processing 2: the quantum emulation of arbitrary Boolean functions

18. Invertible digital circuits and their quantum emulations

19. Quantum measurement 2: general pure states, Bell states

20. Quantum information processing 3

21. More on quantum gates and circuits: those without digital equivalents

22. Quantum algorithms 1

23. Quantum algorithms 2: Simon's algorithm

Appendices

Solutions to Selected Exercises

References

Index

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Author(s)

Biography

Helmut Bez holds a doctorate in quantum mechanics from Oxford University. He is a visiting fellow in Quantum Computation in the Department of Computer Science at Loughborough University, England. He has authored around 50 refereed papers in international journals and a further 50 papers in refereed conference proceedings. He has 35 years' teaching experience in computer science, latterly as reader in geometric computation, Loughborough University. He has supervised/co-supervised 18 doctoral students.

Tony Croft was the founding director of the Mathematics Education Centre at Loughborough University, one of the largest groups of mathematics education researchers in the UK, with an international reputation for the research into and practice of the learning and teaching of mathematics. He is co-author of several university-level textbooks, has co-authored numerous academic papers and edited academic volumes. He jointly won the IMA Gold Medal 2016 for outstanding contribution to the improvement of the teaching of mathematics and is a UK National Teaching Fellow. He is currently emeritus professor of mathematics education at Loughborough University.

(https://www.lboro.ac.uk/departments/mec/staff/academic-visitors/tony-croft/)