发表机构
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文数值模拟了最优锥形量子相位估计（tQPE）用于最小特征值计算，研究了Trotter误差、数字化误差和初始态重叠对算法性能的影响，发现初始态重叠决定采样率，且高Trotter误差下存在时间依赖性和振铃现象。
AI 中文摘要
我们数值实现了最优锥形量子相位估计（以可实现的近似带宽受限DPSS锥形形式）的完整量子电路，用于最小特征值计算，其中哈密顿量时间演化酉算子使用标准Trotter化实现，锥形态使用优化的带宽受限锥形构造。我们在代表性的量子哈密顿量上，通过可处理的精确经典数值量子电路模拟，展示了当tQPE算法参数改变时，锥形QPE在最优相位采样率、绝对误差、最优相位分布的香农熵方面的表现。这些算法参数包括Trotter误差、有限采样、非理想初始态、总演化时间和数字化误差（相位量子比特数）。报告的数值实验包括在4量子比特海森堡量子磁体模型哈密顿量上，使用高达12阶Trotter化，包含多达$\ell=10$个相位量子比特的精度和$m=3$个额外的相位寄存器误差抑制量子比特。我们数值证明了：i) 稳态最优相位采样率由初始态与基态的重叠决定；ii) 对于相位采样概率或整体特征值采样误差率，除非存在高Trotter误差，tQPE没有强烈的演化时间依赖性；iii) tQPE中的近似时间演化酉算子，如同标准QPE，可能导致显著的振铃现象，从而产生非物理的特征值估计。
英文摘要
We numerically implement full quantum circuits of optimal tapered Quantum Phase Estimation (in the form of an implementable approximate bandwidth-limited DPSS taper) for the purpose of minimum eigenvalue computation, where the Hamiltonian time-evolution unitary is implemented using standard Trotterization, and the taper state is constructed using an optimized bandwidth-limited taper. We illustrate, on representative quantum Hamiltonians, with tractable exact classical numerical quantum circuit simulations, how tapered QPE performs with respect to optimal phase sampling rate, absolute error, Shannon entropy of the optimal phase distribution, when the tQPE algorithm parameters are changed. Those algorithm parameters are Trotter error, finite sampling, imperfect initial states, total evolution time, and digitization error (number of phase qubits). The reported numerical experiments include up to $\ell=10$ phase qubits of precision with $m=3$ additional phase-register error suppression qubits, on a $4$-qubit Heisenberg quantum magnet model Hamiltonian, using up to 12th-order Trotterization. We numerically show i) the steady-state optimal phase sampling rate is determined by the initial state overlap with the ground-state, ii) with respect to phase sampling probability, or overall eigenvalue sampling error rate, there is no strong evolution time dependence for tQPE unless there is high Trotter error, iii) the approximated time-evolution unitaries in tQPE, like in standard QPE, can result in substantial ringing, which leads to non-physical eigenvalue estimates.
