Quasiparticle Variational Quantum Eigensolver

TL;DR

This paper introduces a momentum-space variational quantum eigensolver (VQE) framework that efficiently simulates quasiparticle excitations in interacting quantum systems, leveraging symmetries and specialized ansatz to accurately capture excitation spectra.

Contribution

It presents a novel momentum-space VQE approach with a symmetry-adapted ansatz for simulating quasiparticle excitations, validated on the XXZ model with results matching theoretical predictions.

Findings

VQE accurately captures low-lying excitation spectra.

The method estimates quasiparticle velocities consistent with Bethe ansatz.

The approach is extendable to other many-body systems.

Abstract

We propose a momentum-space based variational quantum eigensolver (VQE) framework for simulating quasiparticle excitations in interacting quantum many-body systems on near-term quantum devices. Leveraging translational invariance and other symmetries of the Hamiltonian, we reconstruct the momentum-resolved quasiparticle excitation spectrum through targeted simulation of low-lying excited states using VQE. We construct a translationally symmetric variational ansatz designed to evolve a free-fermion particle-hole excited state with definite momentum $q$ to an excited state of the interacting system at the same momentum, employing a fermionic fast Fourier transform (FFFT) circuit coupled to a Hamiltonian Variational Ansatz (HVA) circuit. Even though the particle number is not explicitly conserved in the variational ansatz, the correct quasiparticle state is reached by energetic optimization. We benchmark the performance of the proposed VQE implementation on the XXZ Hamiltonian, which maps onto the Tomonaga-Luttinger liquid in the fermionic representation. Our numerical results show that VQE can capture the low-lying excitation spectrum of the bosonic quasiparticle/two-spinon dispersion of this model at various interaction strengths. We estimate the renormalized velocity of the quasiparticles by calculating the slope of the dispersion near zero momentum using the VQE-optimized energies at different system sizes, and demonstrate that it closely matches theoretical results obtained from Bethe ansatz. Finally, we highlight extensions of our proposed VQE implementation to simulate quasiparticles in other interacting quantum many-body systems.