Optimization with Programmable Cavity-Mediated Interactions

A broad range of optimization problems can be reduced to finding the ground state of interacting spin models. The ability to configure arbitrary couplings between constituent spins is critical for studying different problem instances in the same system. Our previous work [1] demonstrated cavity-mediated programmable interactions between atomic ensembles to engineer tunable couplings for the XY Hamiltonian. In this poster, we present potential schemes for finding approximate ground states of the classical XY Hamiltonian on our cavity platform, where the quantum quench dynamics of the cavity-mediated interactions amplify states that minimize the XY interaction energy. Additionally, we explore adiabatic approaches and generalize to the variational optimization of sequences that prepare low-temperature states for the XY model. We discuss how these approaches scale with system size and interaction graph complexity. Programmable interactions combined with local addressability provide new tools to study the role that complex structures of entanglement could play in efficiently approximating solutions to hard problems.

1. Periwal, A., Cooper, E. S., Kunkel, P., et al. Nature 600, 630–635 (2021).