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Despite rapid recent progress towards the development of quantum computerscapable of providing computational advantages over classical computers, itseems likely that such computers will, initially at least, be required to runin a hybrid quantum-classical regime. This realisation has led to interest inhybrid quantum-classical algorithms allowing, for example, quantum computers tosolve large problems despite having very limited numbers of qubits. Here wepropose a hybrid paradigm for quantum annealers with the goal of mitigating adifferent limitation of such devices: the need to embed problem instanceswithin the (often highly restricted) connectivity graph of the annealer. Thisembedding process can be costly to perform and may destroy any computationalspeedup. In order to solve many practical problems, it is moreover necessary toperform many, often related, such embeddings. We will show how, for suchproblems, a raw speedup that is negated by the embedding time can nonethelessbe exploited to give a real speedup. As a proof-of-concept example we presentan in-depth case study of a simple problem based on the maximum weightindependent set problem. Although we do not observe a quantum speedupexperimentally, the advantage of the hybrid approach is robustly verified,showing how a potential quantum speedup may be exploited and encouragingfurther efforts to apply the approach to problems of more practical interest.

A Hybrid Quantum-Classical Paradigm to Mitigate Embedding Costs in Quantum Annealing