Quantum Computing: Lecture Notes

TL;DR

This comprehensive set of lecture notes introduces quantum computing concepts, algorithms, complexity, and applications, serving as an educational resource for Master's students in quantum information science.

Contribution

Provides an extensive, structured overview of quantum computation and information, including algorithms, complexity, distributed settings, quantum machine learning, and error correction, with exercises and background material.

Findings

Covers key quantum algorithms like Shor and Grover

Includes discussions on quantum complexity and distributed computing

Provides foundational mathematical background

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, 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.