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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/96379

Title:	Embedding the n-Qubit Projective Clifford Group into a Symmetric Group
Authors:	李金彥;Lee, Chin-Yen
Contributors:	數學系
Keywords:	Clifford群;群表示;標準形;慣性子群;排列表現;Clifford group;presentation;normal form;inertia subgroup;permutation presentation
Date:	2025-03-17
Issue Date:	2025-04-09 18:23:16 (UTC+8)
Publisher:	國立中央大學
Abstract:	n-量子比特Clifford群 Cliffn 和 n-量子比特射影Clifford群 Cn 在量子計算中扮演著關鍵角色，尤其在量子錯誤糾正和量子算法中。然而，即使對於較小的n值，文獻中也很少能找到直接構造這些群的方法。在本論文中，我們利用Clifford閘的標準形來確定Cn 生成元的中央化子。基於這些結果，我們提出將Cn 嵌入到Sym2(4n −1) 中的方法。此外，我們還證明了Cn 中z-閘的中央化子與Cn 的慣性子群同構。;The n-qubit Clifford group, Cliffn, and the n-qubit projective Clifford group, Cn, play pivotal roles in quantum computing, especially in quantum error correction and quantum algorithms. However, methods for directly constructing these groups, even for small values of n, are rarely found in the literature. In this thesis, we use the normal form of Clifford gates to determine the centralizer of the generators of Cn. Based on these results, we propose an embedding of Cn into Sym2(4n −1). Furthermore, we show that the centralizer of the z-gate within Cn is isomorphic to the inertia subgroup of Cn.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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