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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.
- 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
Part I Mathematical Foundations for Quantum Computation
1. Mathematical preliminaries
2. Functions and their application to digital gates
3. Complex numbers
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
Solutions to Selected Exercises
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.