Finding spin-glass ground states using quantum walks

Abstract: Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better than square-root scaling. This makes it practical to use quantum walks for solving such problems, and opens the door for a range of applications on suitable quantum hardware.