Quantum computation and quantum error correction: the theoretical minimum

Mark Wildon (Feb 17 2026).

Abstract: These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow \mathrm{SO}_3(\mathbb{R})$ to illustrate the distinction between states and measurements for a single qubit. We then discuss entanglement and CNOT gates, the Deutsch--Jozsa Problem, and finally quantum error correction, using the Steane $[[7,1,3]]$-code as the main example. The necessary background physics of unitary evolution and Born rule measurements is developed as needed. The circuit model is used throughout.

Arxiv: https://arxiv.org/abs/2602.13876