Tech. Note: Gates, States, and Circuits

Notes on the circuit model of quantum computing. Currently mostly an exposition on the menagerie of quantum gates.

PDF: https://threeplusone.com/gates

Source: https://github.com/gecrooks/on_gates

Release Notes

v0.12 (2026-02-21)

Extensive review of all chapters fixing 100+ spelling, grammar, and math errors. Notable math fixes include: power series signs, CPhase canonical coordinates, Swap-alpha exponents, Hadamard conjugation matrices, XYX/XZX Clifford results, Clifford group product formula, multiplexed gate decomposition formulas, T gate phase, and two-level decomposition normalization. Fixed cross-references and citations.

v0.11 (2024-07-25)

v0.10 (2023-05-26)

v0.9 (2023-03-01)

v0.8 (2022-02-14)

v0.7 (2022-01-12)

v0.6 (2021-07-24)

v5 (2020-11-17)

v4 (2020-06-03)

v3

v2

v1 (2019-05-01)