Reduced quantum circuits for stabilizer states and graph states

• URL: http://arxiv.org/abs/2107.00885v1
• Date: Fri, 2 Jul 2021 07:57:27 GMT
• Title: Reduced quantum circuits for stabilizer states and graph states
• Authors: Marc Bataille
• Abstract summary: We show how to reduce the two-qubit gate count in circuits implementing graph states. All the algorithms described in the paper are implemented in the C language as a Linux command available on GitHub.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the Clifford group. It has shape CX-CZ-P-H-CZ-P-H, where CX (resp. CZ) denotes a layer of $\cnot$ (resp. $\cz$) gates, P a layer of phase gates and H a layer of Hadamard gates. Then we consider a normal form for stabilizer states and we show how to reduce the two-qubit gate count in circuits implementing graph states. Finally we carry out a few numerical tests on classical and quantum computers in order to show the practical utility of our methods. All the algorithms described in the paper are implemented in the C language as a Linux command available on GitHub.

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