Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2609.39602

Warm-Start Iterative QITE for Distribution Network Reconfiguration via Branch-Exchange Encoding

Noah Crum, Pete Pritchard, Tanner Rase, Phillip C. Lotshaw, Shaked Regev, Claudio Girotto, Ananth Kaushik, Paul Smith

quant-phSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We present a hybrid quantum-classical algorithm for distribution network reconfiguration, a combinatorial optimization problem on power distribution networks, that combines a radiality preserving branch-exchange encoding with iterative warm-start quantum imaginary-time evolution to minimize active line losses. The encoding uses a fixed-width binary representation of sequential branch-exchange actions, ensuring that every register outcome decodes to a radial configuration. The quantum subroutine is informed by a surrogate model fit to classically-solved alternating current power flow (ACPF) labels. After a set budget of ACPF solves and circuit samples is exhausted, the algorithm returns the lowest-loss configuration seen. We employ our algorithm on ten test cases, including seven commonly-used benchmark cases and three cases we modified from these and similar standard systems. We include two methods to reduce problem size, which enable extensions of the algorithm to larger networks. We successfully reach minimal-loss configurations for six cases and find configurations with losses from 0.2 percent to 2.18 percent above the reported reference minimal loss for the other four.

Comments
23 pgs, 11 figures

Related papers

Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding

Nowar Alashkar, Cade Kennedy, Phillip C. Lotshaw +6 more

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.

quant-pharXiv:2609.40264•Oct 1, 2026•0 citations

Evaluate Quantum Combinatorial Optimization for Distribution Network Reconfiguration

Ngo, Phuong, Thomas, Christan, Hieu Pham Trung Nguyen +2 more

This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.

arXiv:2208.07513•Aug 16, 2022•0 citations

Iterative warm-start optimization with quantum imaginary time evolution

Phillip C. Lotshaw, Titus Morris, Stuart Hadfield +1 more

Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand, then samples the states to determine an approximately optimal solution. However, promising alternative approaches have considered ``warm-start" and sampling-based methods that instead begin from the best known solution, which can be directly optimized with the quantum computer and updated as new information becomes available, potentially outperforming the fixed ansätze. Here we use these ideas to design a nonvariational quantum algorithm for combinatorial optimization. At each step the algorithm begins with a state superposed around the best known solution, then drives it to lower energy using quantum imaginary time evolution. These nonvariational, initial-state-dependent circuits are determined using analytic equations that are evaluated using only a conventional computer. After implementing the circuits, the state is sampled, potentially obtaining a new best-known solution to use as the initial state at the next iteration. Using simulations of the algorithm solving MaxCut on 3-regular graphs with 30 or fewer vertices and a shot budget of 100 total shots, the approach obtains median solutions within 95\% of the global optimum and finds optimal solutions in 11\% or more of cases, significantly outperforming random and simplified classical search procedures. We discuss several future directions.

quant-pharXiv:2604.26047•Apr 30, 2026•0 citations

Evaluate Quantum Combinatorial Optimization for Distribution Network Reconfiguration

Anh Phuong Ngo, Christan Thomas, Hieu Trung Nguyen +2 more

This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.

North American Power Symposium (NAPS)•Oct 9, 2022•2 citations

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

Carsten Hartmann, Nil Rodellas-Gràcia, Christian Wallisch +5 more

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.

arXiv:2511.00582•Nov 1, 2025•0 citations

Benchmarking Hybrid Quantum-Classical Algorithms for Power Grid Optimization Problems

Igor Gaidai, Rick Mukherjee

Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.

quant-pharXiv:2607.15543•Jul 20, 2026•0 citations
We present a hybrid quantum-classical algorithm for distribution network reconfiguration, a combinatorial optimization problem on power distribution networks, that combines a radiality preserving branch-exchange encoding with iterative warm-start quantum imaginary-time evolution to minimize active line losses. The encoding uses a fixed-width binary representation of sequential branch-exchange actions, ensuring that every register outcome decodes to a radial configuration. The quantum subroutine is informed by a surrogate model fit to classically-solved alternating current power flow (ACPF) labels. After a set budget of ACPF solves and circuit samples is exhausted, the algorithm returns the lowest-loss configuration seen. We employ our algorithm on ten test cases, including seven commonly-used benchmark cases and three cases we modified from these and similar standard systems. We include two methods to reduce problem size, which enable extensions of the algorithm to larger networks. We successfully reach minimal-loss configurations for six cases and find configurations with losses from 0.2 percent to 2.18 percent above the reported reference minimal loss for the other four.
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%1.4\%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%1\%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.
This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand, then samples the states to determine an approximately optimal solution. However, promising alternative approaches have considered ``warm-start" and sampling-based methods that instead begin from the best known solution, which can be directly optimized with the quantum computer and updated as new information becomes available, potentially outperforming the fixed ansätze. Here we use these ideas to design a nonvariational quantum algorithm for combinatorial optimization. At each step the algorithm begins with a state superposed around the best known solution, then drives it to lower energy using quantum imaginary time evolution. These nonvariational, initial-state-dependent circuits are determined using analytic equations that are evaluated using only a conventional computer. After implementing the circuits, the state is sampled, potentially obtaining a new best-known solution to use as the initial state at the next iteration. Using simulations of the algorithm solving MaxCut on 3-regular graphs with 30 or fewer vertices and a shot budget of 100 total shots, the approach obtains median solutions within 95\% of the global optimum and finds optimal solutions in 11\% or more of cases, significantly outperforming random and simplified classical search procedures. We discuss several future directions.
This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming formulation for the reconfiguration of radial distribution network in response to faults in distribution lines. Comparing to existing bus injection model in the literature, our formulation based the branch flows model is theoretically equivalent without needing non-explainable variables, thus being more numerically stable. The network reconfiguration model is then used as a benchmark to evaluate the performance of quantum computing algorithms in real quantum computers. It shows that while current quantum computing algorithms with fast execution time in quantum computers can be a promising solution candidate, its heuristic nature stem from its theoretical foundation should be considered carefully when applying into power grid optimization problems.
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.
Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.