Regular language quantum states
This work provides a new theoretical framework for quantum many-body states, potentially useful for researchers in quantum information and condensed matter physics, but it appears incremental as it builds on existing formal language and tensor network theories.
The paper introduces regular language states, a family of quantum many-body states based on formal languages, encompassing states like GHZ and W states, and develops a theoretical framework to describe them, including criteria for recognition and equivalence.
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.