Preparing Bethe Ansatz Eigenstates on a Quantum Computer

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.

14 pages, 9 figures

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• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Conserved charges in the quantum simulation of integrable spin chains
• Bethe states on a quantum computer: success probability and correlation functions
• Improved variational quantum eigensolver via quasi-dynamical evolution
• Assessment of the variational quantum eigensolver: application to the Heisenberg model
• Benchmarking near-term quantum devices with the Variational Quantum Eigensolver and the Lipkin-Meshkov-Glick model
• State preparation of AGP on a quantum computer without number projection
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Entanglement at the interplay between single- and many-bodyness
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Fractal decompositions and tensor network representations of Bethe wavefunctions