Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space

IF 0.8 3区 数学 Q2 MATHEMATICS
Kazuki Ikeda
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引用次数: 0

Abstract

Using operator algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space. Quantum computation is usually implemented on finite discrete sets, and the purpose of this study is to extend this to theories on arbitrary sets. The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2) is defined on each point of a discrete set. In this study, we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space. The quantum channel is then naturally extended as a net of von Neumann algebras. This allows for a more mathematically rigorous discussion of general theories, including physics and chemistry, which are defined on sets that are not necessarily discrete, from the perspective of quantum computer science.

量子振动:任意拓扑空间上的量子计算
利用算子代数,我们将图上的量子计算理论扩展为任意拓扑空间上的计算理论。量子计算通常是在有限离散集合上实现的,本研究的目的是将其扩展到任意集合上的理论。量子计算机的传统理论可视为简化的代数几何理论,其中 SU(2) 的作用定义在离散集合的每个点上。在本研究中,我们将其扩展为量子纤维理论,其中冯-诺依曼代数的作用定义在任意拓扑空间上。然后,量子通道自然扩展为冯-诺依曼代数的网。这样就可以从量子计算机科学的角度,对包括物理学和化学在内的定义在不一定离散集合上的一般理论进行数学上更严谨的讨论。
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
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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