正则语言量子态
Regular language quantum states
AI总结：
本文提出正则语言量子态，基于正则语言理论，通过矩阵积态描述，建立正则语言态的理论框架，包括等价性定理和移位不变性判定准则。
摘要：
我们引入了正则语言态，一种量子多体态家族。它们由一类称为正则的语言构建，已在计算机科学领域被深入研究。它们可以看作是正则语言中所有单词的叠加，涵盖了物理相关的GHZ-、W-或Dicke态。通过利用正则语言的理论，我们开发了一个描述它们的理论框架。首先，我们将它们用矩阵积态表达，提供高效的识别标准。然后，我们开发了一种规范形式，允许我们为正则语言态的等价性制定基本定理，包括在局部酉操作下。我们还利用张量网络理论，找到一种高效的判据来确定正则语言是否移位不变。
英文摘要：
We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically relevant states such as the GHZ-, W- or Dicke-states. By leveraging the theory of regular languages, we develop a theoretical framework to describe them. First, we express them in terms of matrix product states, providing efficient criteria to recognize them. We then develop a canonical form which allows us to formulate a fundamental theorem for the equivalence of regular language states, including under local unitary operations. We also exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
