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arXiv · 2103.15991

Scaling overhead of embedding optimization problems in quantum annealing

Mario S. Könz·Wolfgang Lechner·Helmut G. Katzgraber·Matthias Troyer
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Abstract

In order to treat all-to-all connected quadratic binary optimization problems (QUBO) with hardware quantum annealers, an embedding of the original problem is required due to the sparsity of the hardware's topology. Embedding fully-connected graphs - typically found in industrial applications - incurs a quadratic space overhead and thus a significant overhead in the time to solution. Here we investigate this embedding penalty of established planar embedding schemes such as minor embedding on a square lattice, minor embedding on a Chimera graph, and the Lechner-Hauke-Zoller scheme using simulated quantum annealing on classical hardware. Large-scale quantum Monte Carlo simulation suggest a polynomial time-to-solution overhead. Our results demonstrate that standard analog quantum annealing hardware is at a disadvantage in comparison to classical digital annealers, as well as gate-model quantum annealers and could also serve as benchmark for improvements of the standard quantum annealing protocol.

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Mario S. Könz, Wolfgang Lechner, Helmut G. Katzgraber, Matthias Troyer. 2021-03-29. Scaling overhead of embedding optimization problems in quantum annealing. https://doi.org/10.1103/prxquantum.2.040322

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