The Bethe Ansatz as a Quantum Circuit

• URL: http://arxiv.org/abs/2309.14430v2
• Date: Wed, 15 May 2024 14:17:48 GMT
• Title: The Bethe Ansatz as a Quantum Circuit
• Authors: Roberto Ruiz, Alejandro Sopena, Max Hunter Gordon, Germán Sierra, Esperanza López,
• Abstract summary: We study the transformation that brings the Bethe ansatz into a quantum circuit. We present a simple set of diagrammatic rules that define a novel Matrix Product State network building Bethe wavefunctions.
• Score: 40.02298833349518
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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