Generators and Relations for 2-Qubit Clifford+T Operators

Published: April 5, 2022Updated: November 15, 2023PDF arXiv

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.

Generators and Relations for 2-Qubit Clifford+T Operators

Xiaoning Bian, Peter Selinger

quant-ph

Published: April 5, 2022Updated: November 15, 2023PDF arXiv

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.