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APS

When quantum relaxation benefits quantum annealing: a case study of ferromagnetic chains with alternating sectors

Anurag Mishra, Daniel A. Lidar, Tameem Albash

Published Jan 1, 2018• 0 citations
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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.
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 the problem of a ferromagnetic chain with sectors of alternating coupling strength. Despite being trivial classically, this is a problem for which the transverse field Ising model is known to exhibit an exponentially decreasing gap in the sector size, suggesting an exponentially decreasing success probability in the sector size if the annealing time is kept fixed. We find that the behavior of the quantum annealing processor departs significantly from this expectation, with the success probability rising and recovering for sufficiently large sector sizes. Rather than correlating with the size of the minimum energy gap, the success probability exhibits a strong correlation 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 of the process and is unrelated to thermal relaxation. Our results indicate that even when the minimum gap is several orders of magnitude smaller than the processor temperature, the system properties at the critical point still determine the performance of the quantum annealer.
As more and more controllable devices equiped in the smart grid, the inceasing scale of binary virables brings time-consuming dimension explosion problems to traditional optimizations problems. As a parallel computing method, quantum computing is valuable for exploration to accelerate the optimization computation. The classic quantum annealer (QA) only can be used for quadratic unconstraint binary optimization (QUBO) problems. This paper is to explore a novel algorithm based on the quantum annealer for grid partition problems. It is a typical large-scale Integer Quadratic Programming (IQP) problems. The proposed quantum algorithm attemped to apply Lagrangian relaxation (LR) and alternating direction method of multipliers (ADMM), to transform an IQP problem to general format of QUBO problems. Some numerical cases of the grid partition are discussed to compare the performance of the proposed algorithm with some typical methods, thus verifing the feasibility and performance of this ADMM-QA algorithm.