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.

4 pages, 4 figures

References in corpus (8)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Mathematical Foundation of Quantum Annealing
• Bounds for the adiabatic approximation with applications to quantum computation
• Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Quantum annealing with antiferromagnetic fluctuations
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet

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• Four-body coupler for superconducting qubits based on Josephson parametric oscillators
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