English

Reduced quantum circuits for stabilizer states and graph states

Quantum Physics 2021-07-05 v1

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\cnot (resp. \cz\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.

Keywords

Cite

@article{arxiv.2107.00885,
  title  = {Reduced quantum circuits for stabilizer states and graph states},
  author = {Marc Bataille},
  journal= {arXiv preprint arXiv:2107.00885},
  year   = {2021}
}

Comments

6 figures, 2 tables, 33 pages. arXiv admin note: text overlap with arXiv:2012.09224

R2 v1 2026-06-24T03:49:58.839Z