Towards Quantum Algorithms for the Optimization of Spanning Trees: The Power Distribution Grids Use Case

TL;DR

This paper explores quantum algorithms, specifically QAOA-based methods, for optimizing the topology of power distribution networks to reduce losses, addressing computational hardness issues in classical approaches.

Contribution

It introduces two novel quantum algorithmic primitives tailored for radial network optimization, advancing quantum solutions for energy grid reconfiguration.

Findings

Quantum algorithms can effectively sample radial network topologies.

Quantum resources required for practical implementation are quantified.

Approximate solutions remain computationally hard classically, but quantum methods show promise.

Abstract

Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many related optimization problems are NP hard, restricting practical applications. In this article, we address the problem of minimizing losses in radial networks, a problem that routinely arises in distribution grid operation. We show that even the computation of approximate solutions is computationally hard and propose quantum optimization as a promising alternative. We derive two quantum algorithmic primitives based on the Quantum Alternating Operator Ansatz (QAOA) that differ in the sampling of network topologies: a tailored sampling of radial topologies and simple sampling with penalty terms to suppress non-radial topologies. We show how to apply these algorithmic primitives to distribution grid reconfiguration and quantify the necessary quantum resources.