测量特罗特误差及其在精确保证哈密顿模拟中的应用

Tatsuhiko N. Ikeda, Hideki Kono, Keisuke Fujii
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引用次数: 0

摘要

特罗特化是数字量子计算机上哈密顿模拟最常用、最方便的近似方法,但对于大型量子系统来说,准确估算其误差在计算上非常困难。在这里,我们开发了一种测量量子电路上无辅助量子比特的特罗特误差的方法,即通过结合 mth 阶和 nth 阶 (m<n) 特罗特化,而不是参考数学误差边界。利用这种方法,我们保证了特罗特化的精度,开发了一种名为 Trotter(m,n) 的算法,其中每个时间步的特罗特误差都在为我们的目的预设的误差容限 ε 范围内。Trotter(m,n) 既适用于与时间无关的哈密顿,也适用于与时间无关的哈密顿,它能在误差容限内自适应地选择几乎最大的步长δt,从而使量子回路保持最浅。以量子自旋链为基准,我们发现自适应选择的 δt 比根据已知的特罗特误差上限推断的δt 大 10 倍左右。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations

Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the mth- and nth-order (m<n) Trotterizations rather than consulting with mathematical error bounds. Using this method, we make Trotterization precision guaranteed, developing an algorithm named Trotter(m,n), in which the Trotter error at each time step is within an error tolerance ε preset for our purpose. Trotter(m,n) is applicable to both time-independent and -dependent Hamiltonians, and it adaptively chooses almost the largest step size δt, which keeps quantum circuits shallowest, within the error tolerance. Benchmarking it in a quantum spin chain, we find the adaptively chosen δt to be about 10 times larger than that inferred from known upper bounds of Trotter errors.
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