Preparing exact eigenstates of the open XXZ chain on a quantum computer

TL;DR

This paper presents a quantum algorithm for preparing Bethe eigenstates of the open XXZ spin chain, enabling quantum simulation of this integrable model with potential applications in quantum computing.

Contribution

It introduces a probabilistic quantum algorithm specifically designed to prepare Bethe states of the open XXZ chain, a novel approach for quantum simulation of integrable models.

Findings

Algorithm requires L+M^2+2M qubits

Success probability decreases with number of down spins

Enables quantum simulation of Bethe states

Abstract

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of $L$ spins with $M$ down spins, which contains a total of $\binom{L}{M}\, 2^{M}\, M!$ terms, the algorithm requires $L+M^2+2M$ qubits.