  Models of interacting many-body quantum systems that may realize new exotic
phases of matter, notably quantum spin liquids, are challenging to study using
even state-of-the-art classical methods such as tensor network simulations.
Quantum computing provides a promising route for overcoming these difficulties
to find ground states, dynamics, and more. In this paper, we argue that
recently developed hybrid quantum-classical algorithms based on real-time
evolution are promising methods for solving a particularly important model in
the search for spin liquids, the antiferromagnetic Heisenberg model on the
two-dimensional kagome lattice. We show how to construct efficient quantum
circuits to implement time evolution for the model and to evaluate key
observables on the quantum computer, and we argue that the method has favorable
scaling with increasing system size. We then restrict to a 12-spin star
plaquette from the kagome lattice and a related 8-spin system, and we give an
empirical demonstration on these small systems that the hybrid algorithms can
efficiently find the ground state energy and the magnetization curve. For these
demonstrations, we use four levels of approximation: exact state vectors, exact
state vectors with statistical noise from sampling, noisy classical emulators,
and (for the 8-spin system only) real quantum hardware, specifically the
Quantinuum H1-1 processor; for the noisy simulations, we also employ error
mitigation strategies based on the symmetries of the Hamiltonian. Our results
strongly suggest that these hybrid algorithms present a promising direction for
resolving important unsolved problems in condensed matter theory and beyond.
