Quantum Computation

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/)

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.