基于样本的量子对角化的机器学习：生成式构型恢复与经典可模拟性边界
Machine learning for sample-based quantum diagonalization: a review of generative configuration recovery and the classical-simulability frontier
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中文总结 AI 辅助
该研究聚焦基于样本的量子对角化，综述相关机器学习方法，经实验发现量子采样子空间精度不优于经典选择组态相互作用，指出其对有效 shots 匮乏的鲁棒性是通用优势，还提及从量子实验学习的可证明量子优势前沿。
中文摘要 AI 辅助
基于样本的量子对角化（SQD），等价于量子选择组态相互作用（QSCI），在两年内已成为容错前量子化学的实用核心：量子处理器采样电子构型，随后在所得行列式子空间中经典对角化多电子哈密顿量。其精度完全由进入该子空间的构型决定，而该选择问题因“优惠券收集者瓶颈”而变得尤为突出，需借助机器学习解决。我们批判性综述了生成式学习选择器的生态系统，按各方法生成的对象及利用的重要信号对其进行组织，并指出一个明显缺口：专为尾部发现设计的奖励比例生成式流网络提议器。随后我们直面该领域核心问题——量子采样器是否优于经典选择组态相互作用——并得出经严格限定的否定结论：在已发表的相同活性空间比较中，强大的经典选择CI与量子采样子空间相当或更优，且旗舰单层电路现已支持多项式时间经典能量估计。我们提炼出基准测试标准，并将该否定结论转化为区域图，随后用全组态相互作用（FCI）精确实验对其进行测试，实验证实一项预测并反驳另一项：廉价先验与精确权重的秩相关性随多参考特征而下降（这是一个可用坐标），但受控单分子噪声扫描显示，我们发现的唯一生成式优势——对有效 shots 匮乏的鲁棒性——是通用的，而非最初混淆对比所暗示的多参考特定效应。最后，我们指出从量子实验中学习，其经典样本复杂度下界是无条件定理，是相邻前沿中唯一可证明存在量子优势但尚未应用于化学的方向。
英文摘要
Sample-based quantum diagonalization (SQD), equivalently quantum-selected configuration interaction (QSCI), has become a centre of gravity of pre-fault-tolerant quantum chemistry: a processor samples electronic configurations and the Hamiltonian is diagonalized classically in the resulting subspace. Accuracy is governed entirely by which configurations enter it -- a machine-learning selection problem, made acute by a coupon-collector bottleneck. We review the generative and learned selectors by what each generates and the signal it exploits, and identify one gap: no reward-proportional generative-flow-network proposer has been built for tail discovery. On the field's central question -- whether the quantum sampler beats classical selected CI -- the negative verdict is not ours to claim: priority belongs to Reinholdt et al. [JCTC 21, 6811 (2025)], and polynomial-time classical estimation of the flagship circuits has reinforced it. We state that verdict at the precision a falsifiable claim requires -- it concerns reproducible, same-active-space comparisons on molecular electronic structure -- and weigh the claims outside those qualifiers. We show that alpha-string weights are not invariant under rotations inside degenerate orbital shells, so determinant counts are undefined until the orbital gauge is declared. We distil a ten-element benchmarking standard and apply it to our own deposit, which returned defects that changed numbers printed here and retracted one from v1. FCI-exact experiments confirm one prediction and refute another: the single generative advantage we find keeps no consistent sign along the dissociation coordinate at device-calibrated noise and reverses under a symmetric readout model. It does beat a noise-matched classical recovery loop on N2 by a margin five seeds cannot resolve, and loses by over a factor of two to a classical selector that needs no sampler.
发表机构
- Universidad Nacional de Colombia（哥伦比亚国立大学）
- SRH University Heidelberg / Munich（SRH海德堡/慕尼黑大学）
- Daita AI
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