We introduce a novel quadratic unconstrained binary optimization (QUBO) formulation for a classical problem in electrical engineering -- the optimal reconfiguration of distribution grids. For a given graph representing the grid infrastructure and known nodal loads, the problem consists in finding the spanning tree that minimizes the total link ohmic losses. A set of constraints is initially defined to impose topologically valid solutions. These constraints are then converted to a QUBO model as penalty terms. The electrical losses terms are finally added to the model as the objective function to minimize. In order to maximize the performance of solution searching with classical solvers, with hybrid quantum-classical solvers and with quantum annealers, our QUBO formulation has the goal of being very efficient in terms of variables usage. A standard 33-node test network is used as an illustrative example of our general formulation. Model metrics for this example are presented and discussed.

中文翻译：

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电力网络最小损耗生成树重构问题的QUBO公式

我们为电气工程中的一个经典问题——配电网的最优重新配置——引入了一种新的二次无约束二元优化 (QUBO) 公式。对于表示电网基础设施和已知节点负载的给定图，问题在于找到最小化总链路欧姆损耗的生成树。一组约束最初被定义为强加拓扑有效的解决方案。然后将这些约束转换为 QUBO 模型作为惩罚项。最后将电气损耗项作为目标函数添加到模型中以最小化。为了最大化使用经典求解器、混合量子经典求解器和量子退火器的解搜索性能，我们的 QUBO 公式的目标是在变量使用方面非常有效。标准的 33 节点测试网络用作我们一般公式的说明性示例。介绍并讨论了此示例的模型度量。