发表机构
IonQ Inc（IonQ公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出轨道旋转阴影层析，将QC-AFQMC经典后处理成本降至多项式级，并证明估计器无偏且方差有界，GPU实现显示并五苯体系后处理仅需两天，大幅提升可扩展性。
AI 中文摘要
量子-经典辅助场量子蒙特卡洛（QC-AFQMC）是利用量子计算机处理强关联电子结构问题的一条有前景的途径，但其可扩展性受到经典后处理瓶颈的限制：在整个AFQMC传播过程中，必须利用测量得到的量子试探态来评估许多游走子的重叠积分、力偏置和局部能量。现有的matchgate-shadow方法避免了通用经典阴影的指数级成本，但对于大系统，其后处理仍然昂贵。在本工作中，我们展示了粒子数守恒的费米子阴影（以轨道旋转阴影实现）能够大幅降低QC-AFQMC的后处理成本。我们推导了重叠积分及其导数的高效估计器，使得每个阴影和游走子的重叠积分与力偏置的缩放为$O(N^3)$，局部能量的缩放为$O(N^4)$，且Cholesky向量为$O(N)$。对于固定的归一化目标行列式，我们还证明了重叠积分估计器是无偏的，其方差上界为$O(\eta)$，其中$\eta$是粒子数，从而为加性重叠误差$\epsilon$提供了$O(\eta/\epsilon^2)$次理想独立测量的充足预算。我们将这些估计器与一种新颖的虚相关能处理以及GPU实现相结合，并演示了使用轨道旋转阴影的QC-AFQMC。对具有(22e, 22o)活性空间和356个总轨道的$\pi$共轭分子（直至并五苯）的性能预测表明，完整的经典后处理工作流程可在8个A100图形处理单元（GPU）上于略多于两天的时间内完成。这些结果显著降低了QC-AFQMC的经典后处理成本，并激励在量子硬件上进一步改进试探态的制备与测量。
英文摘要
Quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) is a promising route to using quantum computers for strongly correlated electronic structure problems, but its scalability is limited by a classical post-processing bottleneck: the measured quantum trial state must be used to evaluate overlaps, force biases, and local energies for many walkers throughout the AFQMC propagation. Existing matchgate-shadow approaches avoid the exponential cost of generic classical shadows, but their post-processing remains expensive for large systems. In this work, we show that particle-number-preserving fermionic shadows, implemented as orbital-rotation shadows, are able to drastically reduce QC-AFQMC post-processing costs. We derive efficient estimators for overlaps and their derivatives, giving $O(N^3)$ scaling for overlaps and force biases and $O(N^4)$ scaling for local energies per shadow and walker and with $O(N)$ Cholesky vector. For fixed normalized target determinants, we also prove that the overlap estimator is unbiased with variance upper bounded by $O(η)$, where $η$ is the particle number, yielding a sufficient budget of $O(η/ε^2)$ ideal independent measurements for additive overlap error $ε$. We combine these estimators with a novel virtual-correlation-energy treatment and a GPU implementation and demonstrate QC-AFQMC using orbital-rotation shadows. Performance projections for $π$-conjugated molecules up to pentacene with a (22e, 22o) active space and 356 total orbitals show that the full classical post-processing workflow can be completed in slightly more than two days on 8$\times$A100 graphics processing units (GPUs). These results significantly reduce classical post-processing costs for QC-AFQMC and motivate further improvements in preparation and measurement of the trial state on quantum hardware.
