TY - JOUR

T1 - Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet

AU - Wauters, Matteo M.

AU - Fazio, Rosario

AU - Nishimori, Hidetoshi

AU - Santoro, Giuseppe E.

N1 - Funding Information:
We acknowledge fruitful discussions with A. Parola and A. Scardicchio. R.F. kindly acknowledges support from the National Research Foundation of Singapore (CRP-QSYNC), the Oxford Martin School, and EU through the project QUIC. G.E.S. acknowledges support from EU FP7 under ERC-MODPHYSFRICT, Grant Agreement No. 320796. Part of the work of H.N. has been supported by the KAKENHI Grant No. 26287086 by the Japan Society for the Promotion of Science.

PY - 2017/8/29

Y1 - 2017/8/29

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.96.022326

DO - 10.1103/PhysRevA.96.022326

M3 - Article

AN - SCOPUS:85028678185

VL - 96

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022326

ER -