  Establishing the nature of the ground state of the Heisenberg antiferromagnet
(HAFM) on the kagome lattice is well known to be a prohibitively difficult
problem for classical computers. Here, we give a detailed proposal for a
Variational Quantum Eigensolver (VQE) intending to solve this physical problem
on a quantum computer. At the same time, this VQE constitutes an explicit
experimental proposal for showing a useful quantum advantage on Noisy
Intermediate-Scale Quantum (NISQ) devices because of its natural hardware
compatibility. We classically emulate noiseless and noisy quantum computers
with either 2D-grid or all-to-all connectivity and simulate patches of the
kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy,
as found by the VQE, approaches the true ground-state energy exponentially as a
function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can
inherently perform their quantum computations in a decoherence-free subspace
that protects against collective longitudinal and collective transversal noise,
adding to the noise-resilience of these algorithms. Nevertheless, the extent of
the effects of other noise types suggests the need for error mitigation and
performance targets alternative to high-fidelity ground-state preparation, even
for essentially hardware-native VQEs.
