Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit, presenting opportunities for the characterization of the decohering environment in a quantum annealing processor.
Quantum annealing in the transverse-field Ising model (TFIM) with open-system dynamics is known to use thermally assisted tunneling to drive computation. However, it is still subject to debate whether quantum systems in the presence of decoherence are more useful than those using classical dynamics to drive computation. We contribute to this debate by introducing the perturbed ferromagnetic chain (PFC), a chain of frustrated subsystems where the degree of frustration scales inversely with the perturbation introduced by a tunable parameter. This gives us an easily embeddable gadget whereby problem hardness can be tuned for systems of constant size. We outline the properties of the PFC and compare classical spin-vector Monte Carlo (SVMC) variants with the adiabatic quantum master equation. We demonstrate that SVMC methods get trapped in the exponentially large first-excited-state manifold when solving this frustrated problem, whereas evolution using quantum dynamics remains in the lowest energy eigenstates. This results in significant differences in ground-state probability when using either classical or quantum annealing dynamics in the TFIM.
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