通过泡利相关编码实现可扩展变分量子优化：在大规模电力需求组合优化中的应用
Qubit-Efficient Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization
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中文总结 AI 辅助
研究针对变分量子算法在大规模问题编码上的局限，提出基于泡利相关编码的可扩展变分框架用于电力需求组合优化，通过两阶段混合公式及数值模拟展示其接近最优性能，还在量子处理器上验证鲁棒性，确立该框架在大规模组合优化中的地位。
中文摘要 AI 辅助
变分量子算法为组合优化提供了一条有前景的途径，但其适用性受到在有限量子比特资源内编码大规模问题挑战的限制。在这项工作中，我们引入了基于泡利相关编码（PCE）的可扩展变分框架，并将其应用于电力需求组合优化。二进制变量通过泡利相关算符的期望值来表示，其编码量子态的多体相关性并提供连续松弛，从而能用少量量子比特进行紧凑表示。我们进一步提出了两阶段混合公式，其中时间平均问题为时间分辨优化提供初始化。数值模拟表明，在从\(m = 18\)到\(10296\)的问题规模上具有接近最优的性能，相对于具有认证最优性的解，归一化成本差距约为\(10^{-4}\)。我们表明性能受连续松弛和离散化之间相互作用的支配：相关器表示的有效分辨率决定了连续损失的改进能多可靠地转化为更好的离散解，更大的系统表现出更一致的行为。最后，我们在俘获离子量子处理器上展示了鲁棒性，尽管存在噪声和有限采样，仍能获得高质量的解。这些结果确立了PCE作为一种基于物理动机且量子比特高效的大规模组合优化框架。
英文摘要
Variational quantum algorithms offer a promising route to combinatorial optimization, but their applicability is limited by the challenge of encoding large-scale problems within restricted qubit resources. In this work, we introduce a qubit-efficient variational framework based on Pauli correlation encoding (PCE) and apply it to electric power demand portfolio optimization. Binary variables are represented through expectation values of Pauli correlation operators, which encode multi-body correlations of the quantum state and provide a continuous relaxation enabling compact representations with few qubits. We further propose a two-stage hybrid formulation, in which a time-averaged problem provides initialization for a time-resolved optimization. Numerical simulations demonstrate near-optimal performance across problem sizes ranging from $m=18$ to $10{,}296$, with normalized cost gaps on the order of $10^{-4}$ relative to solutions with certified optimality. We show that the performance is governed by the interplay between continuous relaxation and discretization: the effective resolution of the correlator representation determines how reliably improvements in the continuous loss translate into better discrete solutions, with larger systems exhibiting more consistent behavior. Finally, we demonstrate robustness on a trapped-ion quantum processor, where high-quality solutions are obtained despite noise and finite sampling. These results establish PCE as a physically motivated and qubit-efficient framework for large-scale combinatorial optimization.
发表机构
- Strategic Technology Center, TISI Inc.（TISI公司战略技术中心）
- Graduate School of Engineering Science, Osaka University（大阪大学工程科学研究科）
- Center for Quantum Information and Quantum Biology, Osaka University（大阪大学量子信息与量子生物学中心）
- Center for Quantum Computing, RIKEN（理化学研究所量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。
