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Quadratic Unconstrained Binary Optimization (QUBO) is a broad class ofoptimization problems with many practical applications. To solve its hardinstances in an exact way, known classical algorithms require exponential timeand several approximate methods have been devised to reduce such cost. With thegrowing maturity of quantum computing, quantum algorithms have been proposed tospeed up the solution by using either quantum annealers or universal quantumcomputers. Here we apply the divide-and-conquer approach to reduce the originalproblem to a collection of smaller problems whose solutions can be assembled toform a single Polynomial Binary Unconstrained Optimization instance with fewervariables. This technique can be applied to any QUBO instance and leads toeither an all-classical or a hybrid quantum-classical approach. When quantumheuristics like the Quantum Approximate Optimization Algorithm (QAOA) are used,our proposal leads to a double advantage: a substantial reduction of quantumresources, specifically an average of ~42% fewer qubits to solve MaxCut onrandom 3-regular graphs, together with an improvement in the quality of theapproximate solutions reached.

Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms