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arXiv:2502.15917 · IEEE Transactions on Power Systems

Qubit-Efficient Quantum Annealing for Stochastic Unit Commitment

Wei Jun Hong, Wangkun Xu, Fei Teng

Published Jun 23, 2026• 1 citation
arXivHTMLPDF

Abstract

Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.

DOI
10.1109/tpwrs.2026.3706404

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Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.
Mixed-integer linear programs (MILPs) are fundamental to power system operations but are challenging to solve due to their NP-hard nature. Quantum annealing, which seeks to find the ground state of an Ising model–a minimization of a quadratic binary function–offers potential speedups for solving combinatorial optimization problems. However, converting MILPs into quadratic unconstrained binary optimization (QUBO) problems often requires lots of slack variables, leading to significant qubit overhead and limiting the capability of quantum annealers. In this work, we propose an efficient formulation approach that generates a QUBO representation of a targeted MILP without introducing auxiliary binary variables. Geometrically, our method approximates the value function of the MILP with a quadratic binary function leveraging a simple convex optimization subroutine. We prove the existence of the QUBO representation, which preserves the MILP’s optimal solution and objective value with the same number of binary variables. The proposed approach is validated on several instances of the security-constrained unit commitment (SCUC) problem, with test cases featuring up to 288 binary variables, demonstrating its efficacy in reducing qubit overhead for quantum-classical hybrid Benders decomposition frameworks.
Uncertainty is fundamental in modern power systems, where renewable generation and fluctuating demand make stochastic optimization indispensable. The chance constrained unit commitment problem (UCP) captures this uncertainty but rapidly becomes computationally challenging as the number of scenarios grows. Quantum computing has been proposed as a potential route to overcome such scaling barriers. In this work, we evaluate the applicability of quantum annealing platforms to the chance constrained UCP. Focusing on a scenario approximation, we reformulated the problem as a mixed integer linear program and solved it using DWave hybrid quantum classical solver alongside Gurobi. The hybrid solver proved competitive under strict runtime limits for large scenario sets (15,000 in our experiments), while Gurobi remained superior on smaller cases. QUBO reformulations were also tested, but current annealers cannot accommodate stochastic UCPs due to hardware limits, and deterministic cases suffered from embedding overhead. Our study delineates where chance constrained UCPs can already be addressed with hybrid quantum classical methods, and where current quantum annealers remain fundamentally limited.
Abstract Uncertainty is fundamental in modern power systems, where renewable generation and fluctuating demand make stochastic optimization indispensable. In stochastic optimization, chance constraints enable the representation of uncertainty in renewable energy sources that affect the dispatch and commitment of bulk generation. This is commonly known as the chance-constrained unit commitment problem (UCP), which rapidly becomes computationally challenging as the number of scenarios grows. Quantum computing has been proposed as a potential route to overcome such scaling barriers. In this work, we evaluate the applicability of quantum annealing platforms to the chance-constrained UCP. Focusing on a scenario approximation, we reformulate the problem as a mixed-integer linear program (MILP) and solve it using D-Wave’s hybrid quantum–classical solver alongside the classical solver Gurobi. The hybrid solver proves competitive under strict runtime limits for large scenario sets (15,000 in our experiments), while Gurobi remains superior on smaller cases. QUBO reformulations have also been tested, but current annealers cannot accommodate stochastic UCPs due to hardware limits, and deterministic cases suffer from embedding overhead. Our study delineates where chance-constrained UCPs can already be addressed with hybrid quantum–classical methods, and where current quantum annealers remain fundamentally limited.
This paper investigates the use of Quantum Annealing (QA) devices for optimizing unit scheduling in renewable energy systems, addressing the challenge of energy balancing with intermittent generation. We compare two approaches for encoding inequality constraints in Quadratic Unconstrained Binary Optimization (QUBO) formulations: (a) the conventional slack-variable-based method and (b) a novel soft-encoding technique called unbalanced penalization. This first application of unbalanced penalization in the energy and power systems domain, aims to disseminate knowledge about near-term applications of quantum-computing and how to make best use of it within the community. Through computational experiments, we find thatUnbalanced Penalizationconsistently outperforms the conventional method of using slack variables by reducing the number of variables in the QUBO formulation. Despite this, its inherent nature penalizes feasible solutions unevenly, preventing the ability to handle much larger problem sizes. More broadly, we observe that both methods-like most pure quantum approaches-struggle with scalability on current QA hardware, as solution quality declines with increasing problem size. In light of these limitations, we assess the feasibility of purely quantum solutions and argue that hybrid approaches remain the most practical path forward.
This paper proposes a learning-based quantum-classical Benders decomposition method for solving large-scale two-stage stochastic unit commitment (UC) problems. The approach integrates a long short-term memory (LSTM) network to approximate subproblem costs and a support vector machine (SVM) classifier to filter dominant Benders cuts, thereby reducing problem size, facilitating quantum computing implementation, and improving scalability. The master problem is reformulated into a quadratic unconstrained binary optimization (QUBO) problem, enabling its solution on quantum hardware. The key contributions are: (i) a quantum-classical decomposition framework tailored for stochastic UC, (ii) an LSTM-based subproblem proxy to facilitate iterations, (iii) an SVM-based cut filtering method to retain only dominant cuts, and (iv) a QUBO reformulation suitable for quantum solvers. Numerical experiments demonstrate that the proposed method significantly reduces computational overhead and quantum resource requirements compared with conventional approaches.
Abstract Quantum computers have strict requirements for the problems that they can efficiently solve. One of the principal limiting factor for the performances of noisy intermediate-scale quantum (NISQ) devices is the number of qubits required by the running algorithm. Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. Numerous techniques have been proposed to achieve such reformulations and, depending on the method chosen, the number of binary variables required, and therefore of qubits, can vary considerably. The aim of this work is to drastically reduce the variables needed for these QUBO reformulations in order to unlock the possibility to efficiently obtain optimal solutions for a class of optimization problems with NISQ devices. This goal is achieved by introducing novel tools that allow an efficient use of slack variables, even for problems with non-linear constraints, without the need to approximate the starting problem. We divide our new techniques in two independent parts, called the iterative quadratic polynomial and the master-satellite methods. Hence, we show how to apply our techniques in case of an NP-hard optimization problem inspired by a real-world financial scenario called Max-Profit Balance Settlement . We follow by submitting several instances of this problem to two D-wave quantum annealers, comparing the performances of our novel approach with the standard methods used in these scenarios. Moreover, this study allows to appreciate several performance differences between the D-wave Advantage and next-generation Advantage2 quantum annealers. We show that the adoption of our techniques in this context allows to obtain QUBO formulations with significantly fewer slack variables, i.e. around 90% less, and D-wave annealers provide considerably higher correct solution rates, which moreover do not decrease with the input size as fast as when adopting standard techniques.