Matrix Product State representation for Slater Determinants and Configuration Interaction States

TL;DR

This paper presents an exact Matrix Product State representation for Slater determinants, enabling efficient quantum state descriptions and potential extensions to more complex configuration interaction states.

Contribution

The paper introduces a novel exact MPS representation for Slater determinants and discusses extensions to include more complex quantum states.

Findings

Exact MPS representation for Slater determinants provided.

Potential for embedding complex configuration interaction states.

Implications for efficient quantum state simulations.

Abstract

Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of Slater determinants as finitely-correlated states is possible. In this paper we analyze this issue and provide an exact Matrix Product representation for Slater determinant states. We also argue possible meaningful extensions that embed more complex configuration interaction states into the description.