Qubit-Efficient Quantum Annealing for Stochastic Unit Commitment

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.