Abstract
The Sherrington-Kirkpatrick model with random $\pm1$ couplings is programmed on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type graph. The performance of the optimizer compares and correlates to simulated annealing. When considering the effect of the static noise, which degrades the performance of the annealer, one can estimate an improvement on the comparative scaling of the two methods in favor of the D-Wave machine. The optimal choice of parameters of the embedding on the Chimera graph is shown to be associated to the emergence of the spin-glass critical temperature of the embedded problem.
Highlights
One tantalizing approach to solve quadratic unconstrained binary optimizations (QUBOs), such as [1,2] in their Ising formulation, is provided by programmable quantum annealing
The D-Wave TwoTM Vesuvius chip hosted at NASA Ames Research Center features 509 working flux qubits connected by 1455 tunable composite qubits acting as Ising-interaction couplings [24], arranged in a nonplanar lattice known as a Chimera graph [25]
We show that random fully connected spin glasses are solvable on Chimera-graph-based annealers through the embedding procedure
Summary
One tantalizing approach to solve quadratic unconstrained binary optimizations (QUBOs), such as [1,2] in their Ising formulation, is provided by programmable quantum annealing. One typical occurrence in applied problems is when the QUBO to be solved is derived from a linear binary optimization problem with a large number of constraints, such as enforced equalities or inequalities between linear relations of variables In this case, the resulting penalty terms in the objective function form intersecting cliques whose minimization might be a hard computational problem for classical algorithms such as simulated annealing [17]. Work we report on the optimal programming guidelines and performance expectation of the D-Wave TwoTM Vesuvius chip, applied to problems defined on fully connected graphs with random couplings in the absence of longitudinal local fields This Hamiltonian corresponds to the Sherrington-Kirkpatrick (SK) model with couplings randomized from a bimodal distribution of values Æ1 [22]. The encoding of the SK model on the D-Wave hardware has very interesting elegant symmetry properties, allowing us to investigate general procedures common to all structured optimizations on annealers, such as the parameter setting of embedding and error correction, which in the general case require heuristic numerical pre- or postprocessing
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