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arXiv 2502.15917quant-phcs.ETcs.SYeess.SY
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用于随机机组组合的量子比特高效量子退火

Qubit-Efficient Quantum Annealing for Stochastic Unit Commitment

Wei Hong, Wangkun Xu, Fei Teng

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AI总结：

提出PHR-ALM方法消除松弛变量，结合量子ADMM分解大规模SUC问题，在D-Wave QPU上实现量子比特和运行时间效率优于经典和基线量子方法。

摘要：

随机机组组合（SUC）已被提出用于管理可再生能源并网带来的不确定性，但这导致了显著的计算复杂性。当使用Benders分解（BD）加速时，主问题变为二进制整数规划，这仍然是NP难的，对经典方法计算要求高。量子退火（QA）以高效求解二次无约束二进制优化（QUBO）问题而闻名，提供了一种潜在解决方案。然而，现有的量子算法依赖松弛变量来处理线性二进制不等式约束，导致量子比特消耗增加和计算效率降低。为解决该问题，本文引入Powell-Hestenes-Rockafellar增广拉格朗日乘子（PHR-ALM）方法，消除了对松弛变量的需求，使量子比特消耗与Benders割的数量增长无关。为进一步减少量子比特开销，应用量子ADMM将大规模SUC分解为较小的块进行顺序求解，该分解不随发电机数量扩展。最后，在4发电机和IEEE 118节点系统上的仿真结果证明了所提算法的可行性和可扩展性，表明在D-Wave QPU平台上，其量子比特和运行时间效率优于经典和基线量子方法。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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