AI 中文总结
研究一维哈伯德模型的量子克里洛夫对角化（QKD），基于低深度约当-维格纳实现，系统研究多因素对其收敛性的影响，给出算法参数选择指南，在IBM量子硬件上演示，证明QKD对研究强关联费米子系统实用且硬件高效。
AI 中文摘要
量子克里洛夫对角化（QKD）已成为一种很有前景的混合量子-经典方法，用于在近期量子设备上估计多体系统的基态性质。本文研究了具有周期性边界条件的一维哈伯德模型的QKD的收敛性、稳定性和硬件性能。基于之前开发的低深度约当-维格纳实现，减少了量子时间演化所需的两比特（CNOT）门数量，系统研究了克里洛夫维数、哈密顿量演化参数、系统大小、相互作用强度和奇异值截断对该方法收敛性的影响。结果表明，QKD的性能受哈密顿量的低能谱结构和数值稳定性之间微妙相互作用的支配。特别是，具有近闭合能隙的系统需要更长的演化时间来有效分辨附近的本征态，同时演化时间、克里洛夫维数、 Trotter数和奇异值截断阈值必须仔细平衡，以避免数值不稳定和累积的时间离散化误差。该分析为在QKD中选择算法参数提供了实用指南。最后，在IBM量子硬件上演示了该算法，实验结果再现了仅使用轻量级读出误差缓解和适度测量预算的理想模拟所预测的收敛趋势。这些结果共同表明，QKD是一种在当前含噪声中等规模量子（NISQ）量子处理器上研究强关联费米子系统的实用且硬件高效的方法。
英文摘要
Quantum Krylov diagonalization (QKD) has emerged as a promising hybrid quantum-classical approach for estimating ground-state properties of many-body systems on near-term quantum devices. In this work, we investigate the convergence, stability, and hardware performance of QKD for the one-dimensional Hubbard model with periodic boundary conditions. Building upon our previously developed low-depth Jordan--Wigner implementation, which reduces the number of two-qubit (CNOT) gates required for quantum time evolution, we perform a systematic study of the influence of the Krylov dimension, Hamiltonian evolution parameters, system size, interaction strength, and singular-value truncation (SVT) on the convergence of the method. Our results show that the performance of QKD is governed by a delicate interplay between the low-energy spectral structure of the Hamiltonian and numerical stability. In particular, systems with near-closing energy gaps require longer evolution times to efficiently resolve nearby eigenstates, while the evolution time, Krylov dimension, Trotter number, and SVT threshold must be carefully balanced to avoid numerical instabilities and accumulated time-discretization errors. This analysis provides practical guidelines for selecting algorithmic parameters in QKD. Finally, we demonstrate the algorithm on IBM quantum hardware, where the experimental results reproduce the convergence trends predicted by ideal simulations using only lightweight readout-error mitigation and a modest measurement budget. Together, these results demonstrate that QKD is a practical and hardware-efficient approach for studying strongly correlated fermionic systems on current NISQ quantum processors.
Comments15 pages, 12 figures
