发表机构
Quantum Research Center, Technology Innovation Institute; Department of Mathematical Sciences, University of Copenhagen（技术创新研究所量子研究中心; 哥本哈根大学数学科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析量子信号处理中的误差传播，提出计算算子-利普希茨常数界的算法及资源感知多项式设计，显著降低T门成本。
AI 中文摘要
量子信号处理（QSP）通过有限次数的多项式变换实现算子函数。除了函数逼近误差外，实际实现还会在编码输入算子以及将门合成到离散容错门集时引入算法误差。我们提供了这些误差的端到端分析，并表明输入误差传播由所实现函数的算子-利普希茨常数 $L_\star$ 控制。然后，我们推导了一种高效的经典算法来计算 $L_\star$ 的紧致下界和上界，并表明这些界进而诱导出与目标总误差兼容的QSP实现所需的总量子资源成本（例如，$T$门数量）的下界和上界。我们进一步设计了一种仅基于多项式系数搜索最小成本多项式的程序，从而为QSP提供了一种资源感知的多项式设计流程。我们通过特征值阈值法对H$_6$分子哈密顿量进行基态能量估计来演示所提出的方法。在测试的硬件配置中，资源感知族改善了总误差预算，并将模拟的$T$门数量相对于通过误差函数逼近获得的标准解析多项式减少了$51.9\\%$--$56.7\\%$。
英文摘要
Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant $L_\star$ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on $L_\star$, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, $T$-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H$_6$ molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled $T$-gate count by $51.9\%$--$56.7\%$ relative to the standard analytical polynomial obtained from an error-function approximation.
CommentsPreliminary version submitted to QIP
