Estimating Bethe roots with VQE

Abstract

Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver (VQE) approach to estimating Bethe roots of the spin-1/2 XXZ quantum spin chain, by using Bethe states as trial states, and treating Bethe roots as variational parameters. In numerical simulations of systems of size up to 6, we obtain estimates for Bethe roots corresponding to both ground states and excited states with up to 5 down-spins, for both the closed and open XXZ chains. This approach is not limited to real Bethe roots.

11 pages + Supplementary Material (Qiskit code); v2: expanded discussion of errors, updated code, version accepted in J. Phys. A

References in corpus (13)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Solving strongly correlated electron models on a quantum computer
• Deriving Boundary S Matrices
• On the completeness of solutions of Bethe's equations
• Fast analytic solver of rational Bethe equations
• Deformed strings in the Heisenberg model
• Algebraic Bethe ansatz for singular solutions
• Algebraic Bethe Circuits
• Preparing exact eigenstates of the open XXZ chain on a quantum computer
• Bethe states on a quantum computer: success probability and correlation functions
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• The Bethe Ansatz as a Quantum Circuit
• Deterministic Bethe state preparation

Cited by in corpus (6)

• Deterministic Bethe state preparation
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Effective Bethe Ansatz for Spin-1 Non-integrable Models
• Spin-$s$ $U(1)$-eigenstate preparation
• Double-bracket quantum algorithms for high-fidelity ground state preparation