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.

Accepted for publication in Quantum

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Cited by in corpus (12)

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• Estimating Bethe roots with VQE
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• Spin-$s$ $U(1)$-eigenstate preparation
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Effective Bethe Ansatz for Spin-1 Non-integrable Models
• Preparation of the single-spinon wave function on a quantum computer