最大独立集问题中Pauli关联编码的拟设基准测试
Benchmarking Ansatze for Pauli Correlation Encoding in the Maximum Independent Set Problem
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中文总结 AI 辅助
本研究针对最大独立集问题，基准测试了多种Pauli关联编码拟设，发现拟设选择对解质量至关重要，减少压缩可显著提升原始解质量，并揭示了可表示性效应在压缩编码中的关键作用。
中文摘要 AI 辅助
5G及新兴6G无线网络日益增长的复杂性，加剧了对能够处理计算上具有挑战性的组合优化问题的可扩展优化技术的需求。虽然量子优化提供了一种有前景的替代方案，但当前近期的量子硬件仍受限于量子比特可用性、噪声和可扩展性约束。Pauli关联编码（PCE）作为一种量子比特高效的优化框架应运而生，通过多项式变量压缩来应对这些挑战。然而，压缩对可表示性和解恢复的影响仍知之甚少。在本工作中，我们研究了这样一个假设：增加压缩比会引入由编码的Pauli可观测量之间的代数闭包关系所产生的可表示性约束。利用最大独立集基准问题，我们评估了多种PCE拟设设计和压缩比。我们发现，拟设的选择对解的质量和可行性都至关重要，其中两个拟设家族始终优于其他方案，并达到了接近0.9的近似比。此外，增加电路重复次数带来的收益有限，甚至可能降低性能。最值得注意的是，通过增加可用量子比特数量来减少压缩，能显著提高原始解的质量，而后处理性能则保持相对稳定。这些发现表明，可表示性效应在压缩的PCE编码中起着重要作用，并为可扩展量子优化中压缩、拟设设计、解码和解质量之间的关系提供了新的见解。
英文摘要
The increasing complexity of 5G and emerging 6G wireless networks has intensified the need for scalable optimization techniques capable of addressing computationally challenging combinatorial problems. While quantum optimization offers a promising alternative, current near-term quantum hardware remains limited by qubit availability, noise, and scalability constraints. Pauli Correlation Encoding (PCE) has emerged as a qubit-efficient optimization framework that addresses these challenges through polynomial variable compression. However, the impact of compression on representability and solution recovery remains poorly understood. In this work, we investigate the hypothesis that increasing compression ratios introduce representability constraints arising from algebraic closure relationships among encoded Pauli observables. Using Maximum Independent Set benchmark problems, we evaluate multiple PCE ansatz designs and compression ratios. We find that ansatz selection is critical to both solution quality and feasibility, with two ansatz families consistently outperforming alternatives and achieving approximation ratios approaching 0.9. Furthermore, increasing circuit repetitions provides limited benefit and can degrade performance. Most notably, reducing compression by increasing the number of available qubits significantly improves raw solution quality, while post-processed performance remains comparatively stable. These findings suggest that representability effects play an important role in compressed PCE encodings and provide new insight into the relationship among compression, ansatz design, decoding, and solution quality in scalable quantum optimization.
发表机构
- KPMG US（毕马威美国）
- KPMG Switzerland（毕马威瑞士）
- IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
机构由 AI 辅助整理，请以论文原文为准。
