Reduced quantum circuits for stabilizer states and graph states

2021/07/02 by Bataille, Marc · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2107.00885

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.

Cited by

• Many-body contextuality and self-testing quantum matter via nonlocal games
• Measurement-Assisted Clifford Synthesis

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