Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several approximate methods have been devised to reduce such cost. With the growing maturity of quantum computing, quantum algorithms have been proposed to speed up the solution by using either quantum annealers or universal quantum computers. Here we apply the divide-and-conquer approach to reduce the original problem to a collection of smaller problems whose solutions can be assembled to form a single Polynomial Binary Unconstrained Optimization instance with fewer variables. This technique can be applied to any QUBO instance and leads to either an all-classical or a hybrid quantum-classical approach. When quantum heuristics like the Quantum Approximate Optimization Algorithm (QAOA) are used, our proposal leads to a double advantage: a substantial reduction of quantum resources, specifically an average of ~42% fewer qubits to solve MaxCut on random 3-regular graphs, together with an improvement in the quality of the approximate solutions reached.

翻译：二次二次控制优化( QUBO) 是一系列广泛的优化问题, 包括许多实际应用。 为了精确地解决其难点, 已知古典算法需要指数化的时间, 并且已经设计了几种近似的方法来降低成本。 随着量子计算日益成熟, 已经提出了量子算法, 通过使用量子肛门或通用量子计算机来加速解决问题。 我们在这里应用“ 分与 ” 方法来减少最初的问题, 将其归结为一系列较小的问题, 这些小问题的解决办法可以组成一个单一的多元二进制非约束的优化实例, 且变量较少。 这一技术可以应用到任何 QUBO 实例, 并导致一种全经典或混合的量子级方法。 当使用量子超常值计算法( QAOA) 等量子超常时, 我们的提案导致双重优势: 量子资源大量减少, 特别是以 ~ 42% 的平均值 来解决随机的3 类方形图的质量解决方案。