发表机构
McMaster University（麦克马斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究通过更好初始化减少量子能量估计中测量成本，提出方差感知排序插入（VarSI）方法，利用协方差字典构建更好非重叠组，有三个变体，经分子基准测试效果良好。
AI 中文摘要
估计哈密顿量期望值的测量成本是变分量子算法的核心瓶颈。分组策略可显著降低成本，重叠技术是该领域的先进方法。重叠分组方法需要对哈密顿量进行非重叠分组（通常由排序插入算法初始化）以及从近似波函数构建协方差字典来指导优化。最近发现不同初始化可能降低重叠方法的测量成本。受此启发，我们引入方差感知排序插入（VarSI），这是一类协方差信息非重叠泡利分组启发式方法以减少测量次数。VarSI分组利用重叠方法已要求的协方差字典来构建更好的非重叠组。我们提出三个变体：全局贪婪分组插入规则、方差信息排序插入类似物以及从排序插入或我们的方差信息变体初始化的局部细化步骤。我们展示了使用我们的VarSI启发式算法生成的分组来初始化使用迭代系数分裂（ICS）算法的重叠方法。对130个哈密顿量的分子基准测试表明，与排序插入相比，VarSI初始化在非重叠测量方面持续改进38%，并且当初始化为VarSI组时，下游ICS结果得到增强。我们发现，与标准排序插入初始化相比，这里考虑的初始化对于ICS实现了高达70%的测量减少，根据所使用的量子比特映射和协方差字典，平均减少9 - 15.3%。这些结果表明，即使最终估计器使用重叠片段，非重叠分组仍然是一个重要的设计步骤。
英文摘要
The measurement cost for estimating expectation values of Hamiltonians is a central bottleneck in variational quantum algorithms. Grouping strategies significantly reduce this cost, with overlapping techniques being the state of the art in the field. Overlapping grouping methods require i) a non-overlapping grouping of the Hamiltonian, typically obtained from the Sorted Insertion (SI) algorithm as initialization, and ii) the construction of covariance dictionaries from approximate wavefunctions to guide the optimization. It was recently shown that different initializations can potentially reduce measurement costs for overlapping methods. Motivated by these findings, we introduce variance-aware SI (VarSI), a family of covariance-informed non-overlapping Pauli grouping heuristics to reduce measurement counts. VarSI grouping leverages the covariance dictionaries, already required by overlapping methods, to construct better non-overlapping groups. We propose three variants: a global greedy grouping insertion rule, a variance-informed SI analog, and a local refinement step initialized from SI or our variance-informed variant. We showcase the use of groupings generated by our VarSI heuristic algorithms to initialize overlapping methods using the iterative coefficient-splitting (ICS) algorithm. Molecular benchmarks with 130 Hamiltonians demonstrate consistent, non-overlapping measurement improvements over SI of 38\% and enhanced downstream ICS results when initialized from VarSI groups. We find that the initializations considered here achieve up to 70\% measurement reductions for ICS, compared to the standard SI initialization with mean reductions of 9--15.3\% depending on qubit mappings and covariance dictionaries used. These results show that non-overlapping grouping remains a consequential design step even when the final estimator uses overlapping fragments.
CommentsMain paper: 8 pages, 1 figure, 2 tables. Supplementary Material: Contact authors or check v1: 22 pages, 4 figures, 5 tables
