Generators and Relations for 2-Qubit Clifford+T Operators

Abstract

We give a presentation by generators and relations of the group of Clifford+T operators on two qubits. The proof relies on an application of the Reidemeister-Schreier theorem to an earlier result of Greylyn, and has been formally verified in the proof assistant Agda.

arXiv commentIn Proceedings QPL 2022, arXiv:2311.08375

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• A Complete Equational Theory for Quantum Circuits
• A Sound and Complete Equational Theory for 3-Qubit Toffoli-Hadamard Circuits
• Minimal Equational Theories for Quantum Circuits