Probing ground state properties of the kagome antiferromagnetic Heisenberg model using the Variational Quantum Eigensolver

TL;DR

This paper demonstrates the potential of the Variational Quantum Eigensolver (VQE) to find ground states of the kagome antiferromagnetic Heisenberg model on quantum computers, showing promising results for small to medium systems.

Contribution

It introduces efficient ansatz circuits for VQE tailored to the KAFH and evaluates their performance through classical simulations across various lattice sizes.

Findings

Fidelity approaches one exponentially with circuit depth for small to medium lattices.

VQE can potentially handle larger lattices beyond classical computational limits.

More variational parameters are needed for larger systems to achieve high fidelity.

Abstract

Finding and probing the ground states of spin lattices, such as the antiferromagnetic Heisenberg model on the kagome lattice (KAFH), is a very challenging problem on classical computers and only possible for relatively small systems. We propose using the Variational Quantum Eigensolver (VQE) to find the ground state of the KAFH on a quantum computer. We find efficient ansatz circuits and show how physically interesting observables can be measured efficiently. To investigate the expressiveness and scaling of our ansatz circuits we used classical, exact simulations of VQE for the KAFH for different lattices ranging from 8 to 24 qubits. We find that the fidelity with the ground state approaches one exponentially in the circuit depth for all lattices considered, except for a 24-qubit lattice with an almost degenerate ground state. We conclude that VQE circuits that are able to represent the ground state of the KAFH on lattices inaccessible to exact diagonalisation techniques may be achievable on near term quantum hardware. However, for large systems circuits with many variational parameters are needed to achieve high fidelity with the ground state.