# Quantum Computing: Lecture Notes

arXiv: https://arxiv.org/abs/1907.09415 · HTML: https://mlsanity.com/paper/1907.09415/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2019.

## Built on by (most cited first, 14 of 14)

- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Quantum Circuit Optimization with AlphaTensor](https://mlsanity.com/paper/2402.14396/) (2024)
- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Quantum Natural Language Generation on Near-Term Devices](https://mlsanity.com/paper/2211.00727/) (2022)
- [Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation](https://mlsanity.com/paper/2301.11936/) (2023)
- [The Quantum Version of Prediction for Binary Classification Problem by Ensemble Methods](https://mlsanity.com/paper/2112.13346/) (2021)
- [Quantum Imitation Learning](https://mlsanity.com/paper/2304.02480/) (2023)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [Fine-Tuning Small Reasoning Models for Quantum Field Theory](https://mlsanity.com/paper/2604.18936/) (2026)
- [Unified Information Dynamic Analysis of Quantum Decision-Making and Search Algorithms: Computational Intelligence Measure](https://mlsanity.com/paper/2306.03233/) (2023)
- [A Catalyst Framework for the Quantum Linear System Problem via the Proximal Point Algorithm](https://mlsanity.com/paper/2406.13879/) (2024)
- [A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices](https://mlsanity.com/paper/2504.13232/) (2025)
- [Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise](https://mlsanity.com/paper/2607.25492/) (2026)

## Abstract (arXiv)

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.