  Quantum annealing is a continuous-time heuristic quantum algorithm for
solving or approximately solving classical optimization problems. The algorithm
uses a schedule to interpolate between a driver Hamiltonian with an
easy-to-prepare ground state and a problem Hamiltonian whose ground state
encodes solutions to an optimization problem. The standard implementation
relies on the evolution being adiabatic: keeping the system in the
instantaneous ground state with high probability and requiring a time scale
inversely related to the minimum energy gap between the instantaneous ground
and excited states. However, adiabatic evolution can lead to evolution times
that scale exponentially with the system size, even for computationally simple
problems. Here, we study whether non-adiabatic evolutions with optimized
annealing schedules can bypass this exponential slowdown for one such class of
problems called the frustrated ring model. For sufficiently optimized annealing
schedules and system sizes of up to 39 qubits, we provide numerical evidence
that we can avoid the exponential slowdown. Our work highlights the potential
of highly-controllable quantum annealing to circumvent bottlenecks associated
with the standard implementation of quantum annealing.
