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Quantum annealing is a continuous-time heuristic quantum algorithm forsolving or approximately solving classical optimization problems. The algorithmuses a schedule to interpolate between a driver Hamiltonian with aneasy-to-prepare ground state and a problem Hamiltonian whose ground stateencodes solutions to an optimization problem. The standard implementationrelies on the evolution being adiabatic: keeping the system in theinstantaneous ground state with high probability and requiring a time scaleinversely related to the minimum energy gap between the instantaneous groundand excited states. However, adiabatic evolution can lead to evolution timesthat scale exponentially with the system size, even for computationally simpleproblems. Here, we study whether non-adiabatic evolutions with optimizedannealing schedules can bypass this exponential slowdown for one such class ofproblems called the frustrated ring model. For sufficiently optimized annealingschedules and system sizes of up to 39 qubits, we provide numerical evidencethat we can avoid the exponential slowdown. Our work highlights the potentialof highly-controllable quantum annealing to circumvent bottlenecks associatedwith the standard implementation of quantum annealing.

Diabatic Quantum Annealing for the Frustrated Ring Model