  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.
