An Index for Quantum Cellular Automata on Fusion Spin Chains

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-03-11 DOI:10.1007/s00023-024-01429-y

Corey Jones, Junhwi Lim

引用次数: 0

Abstract

Interpreting the GNVW index for 1D quantum cellular automata (QCA) in terms of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators of 2D topological codes. We show that for the fusion spin chains built from the fusion category \(\textbf{Fib}\), the index is a complete invariant for the group of QCA modulo finite depth circuits.

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融合自旋链上的量子蜂窝自动机索引

用子因子的琼斯指数来解释一维量子蜂窝自动机（QCA）的 GNVW 指数，就可以把为 QCA 定义的指数推广到更一般的抽象自旋链上。其中包括融合自旋链，它作为全局（分类/MPO）对称下不变的局部算子和二维拓扑代码的边界算子而出现。我们证明，对于由融合范畴 \(\textbf{Fib}\)建立的融合自旋链，索引是 QCA modulo 有限深度电路群的完全不变式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.