Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding
Abstract
Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately 1.4% of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within 1% of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.
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BibTeX
@misc{alashkar2026twostage,
title = {{Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding}},
author = {Nowar Alashkar and Cade Kennedy and Phillip C. Lotshaw and Shaked Regev and Miguel Angel Lopez-Ruiz and Ananth Kaushik and Paul Smith and Claudio Girotto and Martin Roetteler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40264},
eprint = {2609.40264},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40264},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding
AU - Nowar Alashkar
AU - Cade Kennedy
AU - Phillip C. Lotshaw
AU - Shaked Regev
AU - Miguel Angel Lopez-Ruiz
AU - Ananth Kaushik
AU - Paul Smith
AU - Claudio Girotto
AU - Martin Roetteler
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.40264
UR - https://arxiv.org/abs/2609.40264
AB - Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately 1.4% of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within 1% of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.
ER -