Bethe ansatz on a quantum computer?

TL;DR

This paper explores using the Variational Quantum Eigensolver (VQE) with Bethe states to study the anisotropic Heisenberg spin chain on quantum computers, demonstrating initial success with one-magnon states but highlighting challenges with multi-magnon states.

Contribution

It introduces a novel approach of applying Bethe states as variational states within VQE for quantum simulation of spin chains, including constructing exact one-magnon trial states.

Findings

Successful implementation of one-magnon VQE states in Qiskit

Multi-magnon trial states remain challenging to construct

Feasibility of Bethe ansatz-based VQE for small chains demonstrated

Abstract

We consider the feasibility of studying the anisotropic Heisenberg quantum spin chain with the Variational Quantum Eigensolver (VQE) algorithm, by treating Bethe states as variational states, and Bethe roots as variational parameters. For short chains, we construct exact one-magnon trial states that are functions of the variational parameter, and implement the VQE calculations in Qiskit. However, exact multi-magnon trial states appear to be out out of reach.