Hybrid Quantum Annealing for Larger-than-QPU Lattice-structured Problems

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Abstract

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open source D-Wave Hybrid framework, uses a QPU coprocessor operating with generic parameters. Performance is evaluated for standard spin-glass problems on two lattice types with up to 11,616 spin variables, double the size that is directly programmable on any available QPU. The proposed method is shown to converge to low-energy solutions faster than an open source simulated annealing method that is either directly employed or substituted as a coprocessor in the hybrid method. Using newer Advantage QPUs in place of D-Wave 2000Q QPUs is shown to enhance convergence of the hybrid method to low energies and to achieve a lower final energy.

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There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

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Quantum annealing with manufactured spins.

M. W. Johnson, M. H. S. Amin, S Gildert … (2011)

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum annealing. If it could be harnessed, quantum annealing might improve on known methods for solving certain types of problem. However, physical investigation of quantum annealing has been largely confined to microscopic spins in condensed-matter systems. Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin-spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes. Our implementation can be configured in situ to realize a wide variety of different spin networks, each of which can be monitored as it moves towards a low-energy configuration. This programmable artificial spin network bridges the gap between the theoretical study of ideal isolated spin networks and the experimental investigation of bulk magnetic samples. Moreover, with an increased number of spins, such a system may provide a practical physical means to implement a quantum algorithm, possibly allowing more-effective approaches to solving certain classes of hard combinatorial optimization problems.