Abstract
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable, and which are also not well-described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that correspond to real-valued solutions of the Bethe equations. The algorithm is polynomial in the number of T gates and circuit depth, with modest constant prefactors. Although the algorithm is probabilistic, with a success rate that decreases with increasing eigenstate energy, we employ amplitude amplification to boost the success probability. The resource requirements for our approach are lower than other state-of-the-art quantum simulation algorithms for small error-corrected devices, and thus may offer an alternative and computationally less-demanding demonstration of quantum advantage for physically relevant problems.
Highlights
Quantum computers hold the promise of transformative applications in a variety of fields, including cryptanalysis [1], quantum chemistry [2,3], materials science [4,5], and, potentially, combinatorial optimization [6,7]
We propose the study of Bethe ansatz (BA) states on a quantum computer as a computationally less demanding route to the demonstration of quantum advantage for problems relevant to physics, including quantum magnetism [19,20], ultracold atoms [21], and unconventional superconductivity [22]
To achieve quantum advantage for a physically relevant problem, it should be the case that no classical method can deliver results of a comparable accuracy
Summary
Quantum computers hold the promise of transformative applications in a variety of fields, including cryptanalysis [1], quantum chemistry [2,3], materials science [4,5], and, potentially, combinatorial optimization [6,7]. To realize the full potential of quantum computing, large-scale faulttolerant devices will be necessary As these do not yet exist, much recent work has studied possible nearterm applications in the present era of noisy intermediatescale quantum computers (NISQs) [8,9]. The importance of higherorder correlation functions for strongly correlated systems has recently been emphasized [32] The calculation of such observables using a quantum computer in turn hinges on the possibility of efficiently preparing the Bethe ansatz states. The comparison of the computational complexity of these methods to that of the direct construction is an interesting question for future studies, as are probabilistic algorithms for preparing other strongly correlated states [44].
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