Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian

Abstract

We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first- and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.

9 pages, 8 figures

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• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• A dissipative environment may improve the quantum annealing performances of the ferromagnetic p-spin model
• Optimal quantum annealing: A variational shortcut to adiabaticity approach
• Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
• Variationally Scheduled Quantum Simulation
• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Lower Bounds on Quantum Annealing Times
• Detecting the critical point through entanglement in Schwinger model
• Counterdiabatic Reverse Annealing
• On the dynamics of Simulated Quantum Annealing in random Ising chains
• Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing
• Optimization by a quantum reinforcement algorithm
• Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians
• Theoretical survey of unconventional quantum annealing methods applied to adifficult trial problem
• Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
• Improving nonstoquastic quantum annealing with spin-reversal transformations
• Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing
• Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement
• Universal Computation with Quantum Fields
• The anomalously slow dynamics of inhomogeneous quantum annealing
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• Three-Josephson Junctions Flux Qubit Couplings