Simulating the Antiferromagnetic Heisenberg Model on a Spin-Frustrated Kagome Lattice with the Contextual Subspace Variational Quantum Eigensolver

TL;DR

This paper demonstrates how to simulate the ground state of a highly frustrated quantum spin system on a noisy quantum device using advanced subspace reduction and error mitigation techniques, achieving high accuracy.

Contribution

It introduces a novel qubit reduction method with the Contextual Subspace approach combined with DMRG-informed biasing, enabling effective VQE simulations on NISQ hardware for complex spin models.

Findings

Achieved ground state energy estimates with approximately 0.01% error.

Successfully implemented VQE on a Kagome lattice model using error mitigation.

Demonstrated the feasibility of simulating frustrated quantum systems on near-term quantum devices.

Abstract

In this work we investigate the ground state properties of a candidate quantum spin liquid using a superconducting Noisy Intermediate-Scale Quantum (NISQ) device. Specifically, we study the antiferromagnetic Heisenberg model on a Kagome lattice, a geometrically frustrated structure that gives rise to a highly degenerate energy spectrum. To successfully simulate this system, we employ a qubit reduction strategy leveraging the Contextual Subspace methodology, significantly reducing the problem size prior to execution on the quantum device. We improve the quality of these subspaces by using the wavefunctions obtained from low bond dimension Density Matrix Renormalization Group (DMRG) calculations to bias the subspace stabilizers through a symplectic approximate symmetry generator extraction algorithm. Reducing the Hamiltonian size allows us to implement tiled circuit ensembles and deploy the Variational Quantum Eigensolver (VQE) to estimate the ground state energy. We adopt a hybrid quantum error mitigation strategy combining Readout Error Mitigation (REM), Symmetry Verification (SV) and Zero Noise Extrapolation (ZNE). This approach yields high-accuracy energy estimates, achieving error rates on the order of 0.01% and thus demonstrating the potential of near-term quantum devices for probing frustrated quantum materials.