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

TL;DR

This paper introduces a hybrid quantum-classical approach to reduce embedding costs in quantum annealing, enabling potential speedups for solving large, related problems despite current hardware limitations.

Contribution

It proposes a novel hybrid paradigm that mitigates embedding costs in quantum annealers, facilitating practical problem-solving and potential quantum speedups.

Findings

Embedding costs can negate quantum speedup without mitigation.

Hybrid approach shows robustness in exploiting potential quantum advantages.

Case study on maximum weight independent set demonstrates practical applicability.

Abstract

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. In order to solve many practical problems, it is moreover necessary to perform many, often related, such embeddings. We will show how, for such problems, a raw speedup that is negated by the embedding time can nonetheless be exploited to give a real speedup. As a proof-of-concept example we present an in-depth case study of a simple 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 and encouraging further efforts to apply the approach to problems of more practical interest.