Qubit-Efficient Quantum Annealing for Stochastic Unit Commitment

TL;DR

The Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method is introduced to eliminate the need for slack variables so that the qubit consumption becomes independent of the increasing number of bender's cuts, and can significantly reduce qubit requirements and enhance the applicability of QA in SUC problem.

Abstract

Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by the integration of renewable energy sources. When solved by Benders Decomposition (BD), the master problem becomes a binary integer programming which is NP-hard and computationally demanding for classical computational 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 so that the qubit consumption becomes independent of the increasing number of bender's cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks and enables a sequential solution. Consequently, the Quantum-based PHR-ADMM (QPHR-ADMM) can significantly reduce qubit requirements and enhancing the applicability of QA in SUC problem. The simulation results demonstrate the feasibility of the proposed QPHR-ADMM algorithm, indicating its superior time efficiency over classical approaches for large scale QUBO problems under the D-Wave QPU showcases.

Figures (6)

• Figure 1: 4-qubit full-connected QUBO problem and the embedded structure in Chimera unit cell (Ignore the chain strength embedding).
• Figure 2: The hybrid quantum-classical algorithm for SUC (The purple region is decoupled using the proposed QPHR-ADMM algorithm).
• Figure 3: The impact of different coefficients on the number of iterations and convergence (The gray area indicates where the results either fail to converge or converge to incorrect values).
• Figure 4: Qubit overhead of different algorithms with increasing iterations under the BD framwork.
• Figure 5: Convergence of the error (top) and lower bounds (bottom) in the first BD iteration under different values of $\sigma^0$.

Theorems & Definitions (1)

• Remark 1