Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free-energy landscape and use the intuition gained to introduce a classical analog to ARA termed “simulated reverse annealing” (SRA). The close similarity between the two means that they should be compared side by side in applications since SRA could potentially give comparable results. As a solvable example, we analyze how both protocols behave in a family of infinite-range (nondisordered) $p$-spin models. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart (in the range of models considered): SRA succeeds at avoiding discontinuous transitions not only in every case where ARA does, but even in a narrow window of parameters where ARA fails to do so.

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• Adiabatic quantum optimization
• Quantum algorithms & computation
• Quantum statistical mechanics