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arXiv:1708.01026

Benchmarking quantum annealers using symmetries in embedded subgraphs

Dilina Perera, Bhalgamiya, Bhavika, M. A. Novotny

Published Aug 3, 2017• 0 citations
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Abstract

We investigate an efficient, generic method for evaluating the performance of quantum annealing devices that does not require the prior knowledge of the true ground state of the benchmark problem. This approach exploits symmetry properties inherent to the ground states of a composite Hamiltonian comprising the benchmark problem Hamiltonian and its symmetric counterpart. Using this method, we compare the performance of two generations of D-Wave machines. Although we do not observe a noticeable difference in the probability of finding solutions with the required symmetry, our results suggest that the current generation of D-Wave machines notably outperforms its predecessor in finding states closer to those with the required symmetry.

DOI
10.48550/arxiv.1708.01026

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We investigate an efficient, generic method for evaluating the performance of quantum annealing devices that does not require the prior knowledge of the true ground state of the benchmark problem. This approach exploits symmetry properties inherent to the ground states of a composite Hamiltonian comprising the benchmark problem Hamiltonian and its symmetric counterpart. Using this method, we compare the performance of two generations of D-Wave machines. Although we do not observe a noticeable difference in the probability of finding solutions with the required symmetry, our results suggest that the current generation of D-Wave machines notably outperforms its predecessor in finding states closer to those with the required symmetry.
We present an effective method of error mitigation on adiabatic quantum annealing machines. This method involves a mirror symmetric property of the adiabatic quantum device underlying graph. The methodology is tested on different generations of D-Wave annealing devices. An initial Hamiltonian is formed with two mirror- symmetric graphs k = k′, coupled with either ferromagnetic (M > 0) or antiferromagnetic (M < 0) graph edges, and then implemented on the underlying D-Wave Chimera graph. Examining the returned solution states at the end of annealing process, allows one to discard returned states that are not the ground state of the problem Hamiltonian. The approach is applicable to any quantum adiabatic device. We used the method to compare the performances of different generations of adiabatic devices.
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The recent availability of the first commercial quantum computers has provided a promising tool to tackle NP hard problems which can only be solved heuristically with present techniques. However, it is unclear if the current state of quantum computing already provides a quantum advantage over the current state of the art in classical computing. This article assesses the performance of the D-Wave 2X quantum annealer on two NP hard graph problems, in particular clique finding and graph partitioning. For this, we provide formulations as Qubo and Ising Hamiltonians suitable for the quantum annealer and compare a variety of quantum solvers (Sapi, QBSolv, QSage provided by D-Wave Sys, Inc.) to current classical algorithms (METIS, Simulated Annealing, third-party clique finding and graph splitting heuristics) on certain test sets of graphs. We demonstrate that for small graph instances, classical methods still outperform the quantum annealer in terms of computing time, even though the quality of the best solutions obtained is comparable. Nevertheless, due to the limited problem size which can be embedded on the D-Wave 2X chip, the aforementioned finding applies to most of problems of general nature solvable on the quantum annealer. For instances specifically designed to fit the D-Wave 2X architecture, we observe substantial speed-ups in computing time over classical approaches.
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.