Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term

Abstract

We analyze the performance of quantum annealing as formulated by Lechner, Hauke, and Zoller (LHZ), by which a Hamiltonian with all-to-all two-body interactions is reduced to a corresponding Hamiltonian with local many-body interactions. Mean-field analyses show that problematic first-order quantum phase transitions that exist in the original LHZ formulation can be avoided, and thus an exponential speedup is achieved, if we drive the coefficient of the many-body term, which represents the constraint, non-linearly as a function of time. This result applies not only to a simple ferromagnetic model but also to the spin glass problem if a parameter in the spin glass model is chosen appropriately.

arXiv comment4 pages, 4 figures

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• Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme
• Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy
• Four-body coupler for superconducting qubits based on Josephson parametric oscillators
• Multi-tasking through quantum annealing