Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability

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.

Updated to published version

References in corpus (15)

• Decoherence of flux qubits due to 1/f flux noise
• Bounds for the adiabatic approximation with applications to quantum computation
• How Powerful is Adiabatic Quantum Computation?
• Decoherence in adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Consistency Tests of Classical and Quantum Models for a Quantum Annealer
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Simple Glass Models and their Quantum Annealing
• Quantum annealing correction for random Ising problems
• Reexamining classical and quantum models for the D-Wave One processor
• The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions
• Landau-Zener transitions in a two-level system coupled to a finite-temperature harmonic oscillator
• Comment on "Distinguishing Classical and Quantum Models for the D-Wave Device"
• Observation of Co-tunneling in Pairs of Coupled Flux Qubits
• Decoherence induced deformation of the ground state in adiabatic quantum computation

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