Simulating a quasiparticle on a quantum device

TL;DR

This paper introduces a variational quantum algorithm to simulate quasiparticle excitations in many-body systems, leveraging symmetries and quantum parallelism, demonstrated on the transverse field Ising model.

Contribution

It extends the VQE method to construct localized quasiparticle states, enabling exploration of entire excitation bands on quantum devices.

Findings

VQE captures magnon quasiparticles in the paramagnetic phase

VQE identifies topological domain wall excitations

Localized states provide insights into interaction effects

Abstract

We propose a variational approach to explore quasiparticle excitations in interacting quantum many-body systems, motivated by the potential in leveraging near-term noisy intermediate scale quantum devices for quantum state preparation. By exploiting translation invariance and potentially other abelian symmetries of the many-body Hamiltonian, we extend the variational quantum eigensolver (VQE) approach to construct spatially localized quasiparticle states that encode information on the whole excited band, allowing us to achieve quantum parallelism. We benchmark the proposed algorithm via numerical simulations performed on the one-dimension transverse field Ising chain. We show that VQE can capture both the magnon quasiparticles of the paramagnetic phase, and the topologically non-trivial domain wall excitations in the ferromagnetic regime. We show that the localized quasiparticle states constructed with VQE contain accessible information on the full band of quasiparticles, and provide valuable insight into the way interactions renormalize the bare spin flip or domain wall excitations of the simple, trivially solvable limits of the model. These results serve as important theoretical input towards utilizing quantum simulators to directly access the quasiparticles of strongly interacting quantum systems, as well as to gain insight into crucial experimentally measured properties directly determined by the nature of these quasiparticles.