Embedding the n-Qubit Projective Clifford Group into a Symmetric Group

2024/10/14 by Chin-Yen Lee, Lee, Chin-Yen
Mathematics · #math.GR

paper · pdf · doi:10.48550/arxiv.2410.10590

Abstract

In this paper, we construct a symmetric group \rm Sym_2(4ⁿ-1), which contains a subgroup isomorphic to the n-qubit projective Clifford group C_n. To establish this result, we investigate the centralizers of the z gate and the phase gate within the n-qubit projective Clifford group, utilizing the normal form of the Clifford operators. As a byproduct, we also provide a presentation of the inertia subgroup of C_n.

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