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

Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid quantum-classical regime. This realisation has led to interest in hybrid quantum-classical algorithms allowing, for example, quantum computers to solve large problems despite having very limited numbers of qubits. Here we propose a hybrid paradigm for quantum annealers with the goal of mitigating a different limitation of such devices: the need to embed problem instances within the (often highly restricted) connectivity graph of the annealer. This embedding process can be costly to perform and may destroy any computational speedup. We will show how a raw speedup that is negated by the embedding time can nonetheless be exploited to give a practical speedup to certain computational problems. Our approach is applicable to problems in which embeddings can be used multiple times to solve related problems, and may allow quantum speedups to be more readily exploited. As a proof-of-concept we present an in-depth case study of a problem based on the maximum weight independent set problem. Although we do not observe a quantum speedup experimentally, the advantage of the hybrid approach is robustly verified, showing how a potential quantum speedup may be exploited.