We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the p-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second order (p=2, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition (p≥3, i.e., with multispin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards zero when the total annealing time τ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a nonequilibrium Landau-Zener analysis. We also analyze the imaginary-time QA dynamics of the model, finding a 1/τ2 behavior for all finite values of p, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit p(odd)=∞ is also discussed.

Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet / Wauters, Matteo M.; Fazio, Rosario; Nishimori, Hidetoshi; Santoro, Giuseppe E.. - In: PHYSICAL REVIEW. A. - ISSN 2469-9934. - 96:2(2017), pp. 1-14. [10.1103/PhysRevA.96.022326]

Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet

Wauters, Matteo M.;Santoro, Giuseppe E.
2017

Abstract

We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the p-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second order (p=2, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition (p≥3, i.e., with multispin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards zero when the total annealing time τ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a nonequilibrium Landau-Zener analysis. We also analyze the imaginary-time QA dynamics of the model, finding a 1/τ2 behavior for all finite values of p, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit p(odd)=∞ is also discussed.
96
2
1
14
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.022326
https://arxiv.org/abs/1707.02621
Wauters, Matteo M.; Fazio, Rosario; Nishimori, Hidetoshi; Santoro, Giuseppe E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/87939
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