Categorical Tensor Network States
Categorical Tensor Network States
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DOI：
10.1063/1.3672009
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发表时间：
2011-12-01
期刊：
影响因子：
1.6
通讯作者：
Jaksch, Dieter
中科院分区：
文献类型：
--
作者：
Biamonte, Jacob D.;Clark, Stephen R.;Jaksch, Dieter
我们研究使用弦图和范畴论的数学在描述量子态的张量网络。这种方法导致统一的几个想法，以及一些结果和方法，以前没有出现在任何一方的文献。我们的方法使张量网络框架的发展，允许解决量子分解问题，其中有几个吸引人的功能。具体地说，给定一个n体量子态垂直杆psi >，我们提出了一个新的和通用的方法，以因子垂直杆psi >到一个张量网络的明确定义的积木。我们使用的解决方案，以揭露一个以前未知的和大类的量子态，我们证明可以有效地和准确地采样。这种分类张量网络状态的一般框架，其中出现了通用和代数定义的张量的组合，增强了张量网络状态的理论。版权所有2011作者。本文是在知识共享署名3.0未移植许可证下发布的。[doi：10.1063/1.3672009]
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state vertical bar psi >, we present a new and general method to factor vertical bar psi > into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states. Copyright 2011 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [doi:10.1063/1.3672009]