提出一种新型量子可观测量，显著降低优化成本却保持强大功能。
Diagonal Adaptive Non-local Observables on Quantum Neural Networks
- 只用对角可观测量，简化量子电路测量设计。
- 将k局部可观测量复杂度从O(4^k)降至O(2^k)，计算开销减半。
- 适合追求高效变分量子算法的科研人员与工程师。
自适应非局域可观测量（ANOs）表明，使量子可观测量动态化可大幅拓展变分量子算法的函数空间，部分将硬件需求从电路合成转移到测量设计。然而，这一优势伴随参数数量和经典优化成本的急剧上升，因需调整一般厄米可观测量。本文提出一种特殊形式的ANO，仅考虑与量子电路配对的对角可观测量。数学上，这等价于在酉相似变换下的完整ANO空间，因对角矩阵是该空间的典范代表。结果表明，对角型ANO保留了完整ANO的能力，同时将k局部可观测量复杂度从O(4^k)降至O(2^k)，并降低了测量端的经典计算开销。因此，对角ANO在保留大部分完整ANO优势的同时，包含传统变分量子电路（VQC）作为特例。
原文摘要 · Abstract (English)
Adaptive Non-local Observables (ANOs) have shown that making quantum observables dynamic can substantially enlarge the function space of Variational Quantum Algorithms, partly shifting hardware demands from circuit synthesis to measurement design. However, this advantage is accompanied by a steep increase in the number of parameters, as well as the classical optimization cost for varying general Hermitian observables. We propose a special form of ANO that significantly reduces this burden by considering only diagonal observables paired with quantum circuits. Mathematically, this is equivalent to the full ANO of a large parameter space since diagonal matrices are canonical representatives of the ANO space modulo unitary similarity. As a result, Diagonal ANO retains the same capability of full ANO while reducing $k$-local observable complexity from $O(4^k)$ to $O(2^k)$ and lowering the corresponding measurement-side classical computation. In this sense, diagonal ANO preserves much of the benefit of full ANO while encompassing conventional VQCs as a special case.
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