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

In this talk, I show a proof-of-principle demonstration of two medium-term hybrid quantum algorithms for finding ground states, unitary variational quantum phase estimation (UVQPE) and observable dynamical mode decomposition (ODMD). Both algorithms use real-time evolution on a quantum device to generate a small linear algebra problem that is solved classically to find an approximate ground state and corresponding energy. I demonstrate both algorithms on a frustrated 8-spin Heisenberg model, consisting of one "star" of the square kagome lattice, using simulations on the Quantinuum H1 processor and the corresponding noisy emulator. Even in the presence of noise, both algorithms rapidly converge, giving good approximations to the ground state of the model. I furthermore show how, using the spin-symmetry of the Heisenberg model, these algorithms can also be used to compute the magnetization curve.