The Bethe Ansatz as a Quantum Circuit
Abstract
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of plane wave superpositions. Previously, it has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. An analytical derivation of the quantum gates that form the circuit was lacking however. Here we present a comprehensive study of the transformation that brings the Bethe ansatz into a quantum circuit, which leads us to determine the analytical expression of the circuit gates. As a crucial step of the derivation, we present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions. Remarkably, this provides a new perspective on the equivalence between the coordinate and algebraic versions of the Bethe ansatz.
Cite
@article{arxiv.2309.14430,
title = {The Bethe Ansatz as a Quantum Circuit},
author = {Roberto Ruiz and Alejandro Sopena and Max Hunter Gordon and Germán Sierra and Esperanza López},
journal= {arXiv preprint arXiv:2309.14430},
year = {2024}
}
Comments
Accepted for publication in Quantum