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Problem-Structure-Informed Quantum Approximate Optimization Algorithm for Large-Scale Unit Commitment with Limited Qubits

Jingxian Zhou, Ziqing Zhu, Linghua Zhu, Siqi Bu

TL;DR

The paper addresses the large-scale Unit Commitment Problem (UCP) under quantum hardware constraints by introducing a problem-structure-informed QAOA (PSI-QAOA) that leverages power-system topology to decompose UCP into parallel subproblems solvable with a limited number of qubits. It maps UCP to a QUBO with binary variables $s_{t,i}$ and $on_{t,i}$ and penalties $A,B,C,D$, then builds an Ising model and applies a three-stage decomposition and refinement, including a gain-based subproblem selection and QIRO-enhanced QAOA on subproblems with size $H$. The approach uses Ising-model construction and simplification to a coarser graph with a minimum size $m$, followed by fidelity-preserving interpolation via operator $R$ and partial solving of prioritized subgraphs. Experiments on IEEE benchmarks show substantial generation-cost reductions relative to MILP and simulated annealing, with performance benefits growing in certain sparsity regimes, suggesting a promising pathway for scalable quantum-assisted optimization in future power systems.

Abstract

As power systems expand, solving the Unit Commitment Problem (UCP) becomes increasingly challenging due to the dimensional catastrophe, and traditional methods often struggle to balance computational efficiency and solution quality. To tackle this issue, we propose a problem-structure-informed Quantum Approximate Optimization Algorithm (QAOA) framework that fully exploits the quantum advantage under extremely limited quantum resources. Specifically, we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems, each solvable in parallel by limited number of qubits. This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse. Consequently, our approach can be readily extended to future power systems that are larger and more complex.

Problem-Structure-Informed Quantum Approximate Optimization Algorithm for Large-Scale Unit Commitment with Limited Qubits

TL;DR

The paper addresses the large-scale Unit Commitment Problem (UCP) under quantum hardware constraints by introducing a problem-structure-informed QAOA (PSI-QAOA) that leverages power-system topology to decompose UCP into parallel subproblems solvable with a limited number of qubits. It maps UCP to a QUBO with binary variables and and penalties , then builds an Ising model and applies a three-stage decomposition and refinement, including a gain-based subproblem selection and QIRO-enhanced QAOA on subproblems with size . The approach uses Ising-model construction and simplification to a coarser graph with a minimum size , followed by fidelity-preserving interpolation via operator and partial solving of prioritized subgraphs. Experiments on IEEE benchmarks show substantial generation-cost reductions relative to MILP and simulated annealing, with performance benefits growing in certain sparsity regimes, suggesting a promising pathway for scalable quantum-assisted optimization in future power systems.

Abstract

As power systems expand, solving the Unit Commitment Problem (UCP) becomes increasingly challenging due to the dimensional catastrophe, and traditional methods often struggle to balance computational efficiency and solution quality. To tackle this issue, we propose a problem-structure-informed Quantum Approximate Optimization Algorithm (QAOA) framework that fully exploits the quantum advantage under extremely limited quantum resources. Specifically, we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems, each solvable in parallel by limited number of qubits. This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse. Consequently, our approach can be readily extended to future power systems that are larger and more complex.

Paper Structure

This paper contains 7 sections, 3 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Methodology
  4. Ising Model Construction and Simplification
  5. Ising Model Refinement and QAOA Implementation
  6. Case Study
  7. Conclusion

Figures (1)

  • Figure 1: Detailed description of PSI-QAOA. The power system topology (Step 1) with red dots as units and solid lines as circuits is mapped to a QUBO based Ising model (Step 2), where blue dots represent decision variables and dashed lines indicate node relationships based on the objective function and constraints. The original graph (Step 3) is simplified to a coarsest graph (Step 4), which is solved by MQLib for an initial solution (Step 5). This is followed by refinement of the Ising model with gain via QIRO (Step 6 to Step 8), and finally mapping back to the original power system optimal schedule (Step 9).