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Models of interacting many-body quantum systems that may realize new exoticphases of matter, notably quantum spin liquids, are challenging to study usingeven state-of-the-art classical methods such as tensor network simulations.Quantum computing provides a promising route for overcoming these difficultiesto find ground states, dynamics, and more. In this paper, we argue thatrecently developed hybrid quantum-classical algorithms based on real-timeevolution are promising methods for solving a particularly important model inthe search for spin liquids, the antiferromagnetic Heisenberg model on thetwo-dimensional kagome lattice. We show how to construct efficient quantumcircuits to implement time evolution for the model and to evaluate keyobservables on the quantum computer, and we argue that the method has favorablescaling with increasing system size. We then restrict to a 12-spin starplaquette from the kagome lattice and a related 8-spin system, and we give anempirical demonstration on these small systems that the hybrid algorithms canefficiently find the ground state energy and the magnetization curve. For thesedemonstrations, we use four levels of approximation: exact state vectors, exactstate vectors with statistical noise from sampling, noisy classical emulators,and (for the 8-spin system only) real quantum hardware, specifically theQuantinuum H1-1 processor; for the noisy simulations, we also employ errormitigation strategies based on the symmetries of the Hamiltonian. Our resultsstrongly suggest that these hybrid algorithms present a promising direction forresolving important unsolved problems in condensed matter theory and beyond.

Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor