Variational Coherent Quantum Annealing

We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer, a method we call variational coherent quantum annealing (VCQA). It involves optimizing the schedule functions governing the quantum dynamics by employing a piecewise family of tailored functions. We also introduce auxiliary Hamiltonians that vanish at the beginning and end of the evolution to increase the energy gap during the process, subsequently reducing the algorithm times. We develop numerical tests using z-local terms as the auxiliary Hamiltonian while considering linear, cyclic, and star connectivity. Moreover, we test our algorithm for a non-stoquastic Hamiltonian such as a Heisenberg chain, showing the potential of the VCQA proposal in different scenarios. In this manner, we achieve a substantial reduction in the ground-state error with just six variational parameters and a duration within the device coherence times. Therefore, the proposed VCQA paradigm offers exciting prospects for current quantum annealers.