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arXiv 2206.06409quant-ph
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复合量子模拟

Composite Quantum Simulations

Matthew Hagan, Nathan Wiebe

AI总结:

本文提出一个复合量子模拟框架,通过划分哈密顿量项并结合QDrift与高阶Trotter-Suzuki公式,降低门计数,并证明其与理想模拟通道的金刚石距离界限及成本渐近上界。

摘要:

在本文中,我们提供了一个框架,用于将多种量子模拟方法(如Trotter-Suzuki公式和QDrift)组合成单一的复合通道,该通道建立在较早的合并思想之上,以减少门计数。我们方法的核心思想是使用一种划分方案,将哈密顿量项分配给模拟通道中的Trotter或QDrift部分。这使我们能够使用QDrift模拟数量众多但规模较小的项,同时使用高阶Trotter-Suzuki公式模拟较大的项。我们证明了复合通道与理想模拟通道之间金刚石距离的严格界限,并展示了在何种条件下,对于概率性项划分和确定性划分,实现复合通道的成本在渐近意义上由构成它的方法所上界限制。最后,我们讨论了确定划分方案的策略以及在同一框架内纳入不同模拟方法的方法。

英文摘要:

In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the Composite channel and the ideal simulation channel and show under what conditions the cost of implementing the Composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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