Designing Quantum Annealing Schedules with Bayesian Optimization

In Quantum Annealing (QA) the ground state of a target Hamiltonian is prepared by continuously deforming an initial Hamiltonian, which has an easy-to-prepare ground state, into the target Hamiltonian. The time evolution generated by this time dependent Hamiltonian depends on the schedule by which this transformation is performed. We investigate the use of Bayesian Optimization (BO), a global optimization design strategy useful for optimizing expensive-to-evaluate functions, to design optimized QA schedules. We test different parametrizations of QA schedules and use BO to optimize them in terms of several figures of merit. We numerically demonstrate significant improvements using BO designed QA schedules for the p-spin model. In addition, BO is used to design paths for Reverse Annealing (RA), a variant of QA which uses an approximation of the final ground state as the initial state, which has been shown to enable an exponential speedup over QA for the p-spin model. BO is able to design a RA schedule which achieves such a speedup without a priori knowing the spectral properties of the system. Finally, we use BO designed QA to solve combinatorial optimization problems and benchmark our results using Simulated Annealing.