Abstract
Closed-system quantum annealing is expected to sometimes fail spectacularly in solving simple problems for which the gap becomes exponentially small in the problem size. Much less is known about whether this gap scaling also impedes open-system quantum annealing. Here, we study the performance of a quantum annealing processor in solving such a problem: a ferromagnetic chain with sectors of alternating coupling strength that is classically trivial but exhibits an exponentially decreasing gap in the sector size. The gap is several orders of magnitude smaller than the device temperature. Contrary to the closed-system expectation, the success probability rises for sufficiently large sector sizes. The success probability is strongly correlated with the number of thermally accessible excited states at the critical point. We demonstrate that this behavior is consistent with a quantum open-system description that is unrelated to thermal relaxation, and is instead dominated by the system’s properties at the critical point.
Highlights
Closed-system quantum annealing is expected to sometimes fail spectacularly in solving simple problems for which the gap becomes exponentially small in the problem size
A commonly cited failure mode of closed-system quantum annealing is the exponential closing of the quantum gap with increasing problem size
We did so by studying the example of a ferromagnetic Ising chain with alternating coupling-strength sectors, whose gap is exponentially small in the sector size, on a quantum annealing device
Summary
Since the transverse field generates only local spin flips, QA is likely to get stuck in a local minimum with domain walls (antiparallel spins resulting in unsatisfied couplings) in the disordered (light) sectors, if tf is less than exponential in n We note that this mechanism, in which large local regions order before the whole is well-known in disordered, geometrically local optimization problems, giving rise to a Griffiths phase[22]. The features of the DW2X success probability results, the exponential fall and rise with n, and the position of the minimum, can be explained in terms of the number of single-fermion states that lie within the temperature energy scale at the critical point. ΦkðsÞðA À BÞðA þ BÞ 1⁄4 λ2kðsÞΦkðsÞ; ð5Þ where the matrices A and B are tridiagonal and are given in
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