发表机构
IBM Research India（印度IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
DF-SQD是一种混合量子经典算法，通过推导确定性辅助场电路改进采样量子对角化，在N₂和铁硫簇哈密顿量上，以更少采样次数、更浅电路实现更高精度与更快速度。
AI 中文摘要
基于采样的量子对角化方法利用以量子为中心的超级计算平台在量子计算机上采样比特串以进行哈密顿量投影，随后在经典计算机上对哈密顿量进行对角化，从而估计其本征值与本征向量。当前量子设备中，当带有误差缓解支持的浅量子电路能获得更优结果，且该算法具备收敛性证明或某种可解释实验可信度的方法时，该算法才具有实用性。本文提出DF-SQD，这是一种混合算法，可从两电子张量的选定双因子分解叶中推导确定性辅助场电路。这些电路提出占据数构型，而选定的组态相互作用会评估原始活性空间哈密顿量，并可对后续提议轮次进行重新聚焦。在N₂（32量子比特；6-31G基组）和40量子比特的[Fe₂S₂(SCH₃)₄]²⁻活性空间哈密顿量上，我们表明DF-SQD在模拟器和硬件运行中，均能在使用浅的保数量电路的同时，提升从采样行列式空间获得的能量。对于N₂，DF-SQD的精度提升了45倍，且子空间缩小了11.23%；由于其能在更少的采样次数下采样更优的比特串，在量子设备上比SQD快2.93倍。对于铁硫簇，DF-SQD在40万次采样下生成了2.21亿的子空间维度，而SQD需要150万次采样才能生成2.38亿的子空间，因此在硬件上可见，我们以减少3.75倍的采样次数实现了更优的子空间恢复。在匹配的5000万子空间维度下，DF-SQD的精度提升了1.32倍（相较于标准SQD实现了24.5%的相对误差降低）。综上，我们的方法能够用更浅的电路获得更优结果，具备采样效率，使用组态恢复（因此具备针对性误差缓解），且我们观察到了经验收敛性。
英文摘要
Sampling-based quantum diagonalization method exploits Quantum-centric supercomputing platforms to sample bitstrings for Hamiltonian projection on a quantum computer, and then classically diagonalize the Hamiltonian to estimate the eigenvalues and eigenvectors. In current quantum devices an algorithm is useful when shallow quantum circuits with error mitigation support can discover better results while having either a proof of convergence or some method to explain trust in experiment. In this paper, we introduce DF-SQD, a hybrid algorithm that derives deterministic auxiliary-field circuits from selected double-factorization leaves of the two-electron tensor. The circuits propose occupation-number configurations, while selected configuration interaction evaluates the original active-space Hamiltonian and can recentre subsequent proposal rounds. On N2 (32 qubits; 6-31G basis) and a 40-qubit [Fe2S2(SCH3)4]2- active-space Hamiltonian, we show that DF-SQD improves the energy obtained from sampled determinant spaces while using shallow number-preserving circuits in both simulator and hardware runs. For N2, DF-SQD is 45x more accurate with a 11.23\% smaller subspace, and due to its ability to sample better bitstrings at lesser shots it is 2.93x faster than SQD in quantum devices. For the iron-sulfur cluster, DF-SQD generated a subspace dimension of 221M with 400K shots, while SQD needed 1.5M shots to generate a 238M subspace, thus we have better subspace recovery evident from the hardware at 3.75x reduced shots. At a matched 50M subspace dimension, DF-SQD is 1.32x more accurate (achieves a 24.5\% relative error reduction over standard SQD). So overall, our method is able to discover better results with shallower circuits, is sample efficient, uses configuration recovery (so has targeted error mitigation) and we have empirical convergence observation.
