Solving Optimal Power Flow using a Variational Quantum Approach

2025-08-29

AI Summary

This work addresses the large-scale nonconvex Optimal Power Flow (OPF) problem in power systems—a computationally challenging quadratic-constrained quadratic program where scalability and global optimality are difficult to reconcile. We propose the first primal-dual variational quantum circuit framework: two parameterized quantum circuits independently encode the primal variables and Lagrange multipliers (dual variables), while the Lagrangian function is mapped to the expectation value of a quantum observable. A classical gradient-based optimizer jointly updates both sets of parameters to locate a saddle point. Crucially, we introduce a variable permutation strategy that enforces a banded structure on the observable, substantially reducing measurement overhead. Implemented as a hybrid quantum-classical algorithm in PennyLane, our method yields high-quality OPF solutions on the IEEE 57-bus system, demonstrating its potential to enhance efficiency and practical applicability for constrained optimization in power systems.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

The optimal power flow (OPF) is a large-scale optimization problem that is central in the operation of electric power systems. Although it can be posed as a nonconvex quadratically constrained quadratic program, the complexity of modern-day power grids raises scalability and optimality challenges. In this context, this work proposes a variational quantum paradigm for solving the OPF. We encode primal variables through the state of a parameterized quantum circuit (PQC), and dual variables through the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. An OPF solution can be found by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. We pursue saddle points of the Lagrangian in a hybrid fashion. Gradients of the Lagrangian are estimated using the two PQCs, while PQC parameters are updated classically using a primal-dual method. We propose permuting primal variables so that OPF observables are expressed in a banded form, allowing them to be measured efficiently. Numerical tests on the IEEE 57-node power system using Pennylane's simulator corroborate that the proposed doubly variational quantum framework can find high-quality OPF solutions. Although showcased for the OPF, this framework features a broader scope, including conic programs with numerous variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.

Problem

• Solving large-scale optimal power flow optimization problems
• Addressing scalability and optimality challenges in power grids
• Proposing variational quantum methods for constrained optimization

Innovation

• Variational quantum paradigm for OPF
• Dual PQC encoding for Lagrangian optimization
• Banded observables for efficient measurement