Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

TL;DR

This paper introduces a hybrid quantum-classical method combining NLCE and VQE to study quantum many-body systems in the thermodynamic limit, successfully applying it to the transverse-field Ising model.

Contribution

It presents a novel integration of NLCE with VQE as a cluster solver, enabling efficient ground-state energy calculations in the thermodynamic limit.

Findings

NLCE+VQE converges to traditional NLCE results with sufficient VQE layers.

The approach connects quantum many-body techniques with hybrid quantum algorithms.

Demonstrates feasibility on existing quantum hardware.

Abstract

We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the VQE algorithm is used as a cluster solver within the NLCE. We test our hybrid quantum-classical algorithm (NLCE$+$VQE) for the ferromagnetic transverse-field Ising model on the one-dimensional chain and the two-dimensional square lattice. The calculation of ground-state energies on each open cluster demands a modified Hamiltonian variational ansatz for the VQE. One major finding is convergence of NLCE$+$VQE to the conventional NLCE result in the thermodynamic limit when at least $N/2$ layers are used in the VQE ansatz for each cluster with $N$ sites. Our approach demonstrates the fruitful connection of techniques known from correlated quantum many-body systems with hybrid algorithms explored on existing quantum-computing devices.