Hamiltonian Simulation with Random Inputs
Hamiltonian Simulation with Random Inputs
复制标题
随机输入的哈密顿模拟
DOI：
10.1103/physrevlett.129.270502
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发表时间：
2022
影响因子：
8.6
通讯作者：
Childs, Andrew M.
中科院分区：
文献类型：
--
作者：
Zhao, Qi;Zhou, You;Shaw, Alexander F.;Li, Tongyang;Childs, Andrew M.
数字量子模拟的算法误差通常是根据实际和理想演化算子之间的谱范数距离来研究的。在实践中，这种最坏情况误差分析可能是不必要的悲观。为了解决这个问题，我们提出了一个具有随机初始状态的哈密顿模拟的平均情况性能理论。我们将平均情况误差与乘法误差的Frobenius范数联系起来，并给出乘积公式（PF）和截断泰勒级数方法的上界。作为应用，我们估计了一般格哈密顿和局部哈密顿的数字哈密顿模拟的平均情况误差。特别地，对于带自旋的最近邻海森堡链，PF方法和泰勒级数方法的误差从最坏情况二次减小到平均值。数值证据表明，该理论准确地表征了具体模型的平均误差。并将所得结果应用于量子置乱仿真中的误差分析。
The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for the digital Hamiltonian simulation of general lattice Hamiltonians and-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain withspins, the error is quadratically reduced fromin the worst case toon average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.