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

Matteo M. Wauters, Rosario Fazio, Hidetoshi Nishimori, Giuseppe E. Santoro

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Article number022326
JournalPhysical Review A
Issue number2
Publication statusPublished - 2017 Aug 29
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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