Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field

Abstract

We show, for quantum annealing, that a certain type of inhomogeneous driving of the transverse field erases first-order quantum phase transitions in the p-body interacting mean-field-type model with and without longitudinal random field. Since a first-order phase transition poses a serious difficulty for quantum annealing (adiabatic quantum computing) due to the exponentially small energy gap, the removal of first-order transitions means an exponential speedup of the annealing process. The present method may serve as a simple protocol for the performance enhancement of quantum annealing, complementary to non-stoquastic Hamiltonians.

4 pages, 5 figures. To be published in J. Phys. Soc. Jpn

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• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• Counterdiabatic Reverse Annealing
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Theoretical survey of unconventional quantum annealing methods applied to adifficult trial problem
• Quantum Phase Transition in Fully-Connected Quantum Wajnflasz-Pick Model