Quantum Computing: Lecture Notes

Abstract

This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 4 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, a chapter about quantum machine learning, one about stabilizer states and Clifford circuits, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.

Version 6: added a new chapter about stabilizer states and Clifford circuits, more exercises, and many small improvements of the text throughout

References in corpus (3)

• Quantum algorithm for solving linear systems of equations
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers

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• Quantum Distributed Complexity of Set Disjointness on a Line
• Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs
• Near-Optimal Quantum Algorithms for String Problems
• Unitary Subgroup Testing
• An Economic Model for Quantum Key-Recovery Attacks against Ideal Ciphers
• Sublinear quantum algorithms for estimating von Neumann entropy
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks
• Global Optimum Search in Quantum Deep Learning