The Trotter step size required for accurate quantum simulation of quantum chemistry
The Trotter step size required for accurate quantum simulation of quantum chemistry
复制标题
量子化学精确量子模拟所需的 Trotter 步长
DOI：
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发表时间：
2014
影响因子：
1
通讯作者：
M. Troyer
中科院分区：
文献类型：
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作者：
D. Poulin;M. Hastings;D. Wecker;N. Wiebe;Andrew C. Doberty;M. Troyer
分子模拟是量子计算机的一个广泛预期的应用。然而，最近的研究[1，2]给这一希望蒙上了阴影，揭示了这种模拟的门计数的复杂性随着自旋轨道N的数量增加而增加，这甚至对于中等大小的分子N = 100也变得令人望而却步。这项研究部分是基于随机人工分子的合奏所需的特罗特步骤的缩放分析。在这里，我们重新审视了这个分析，发现在我们研究的真实的模型分子的最坏情况下，标度更接近N6，这表明随机系综不能准确地捕捉真实世界分子的统计特性。由于平均效应，实际缩放可能比这好得多。然后，我们提出了一种替代的模拟方案，并表明它有时可以优于现有的计划，但这种可能性取决于模拟分子的细节至关重要。我们使用[1]的合并方案的一个版本获得了进一步的改进;该方案基于对不同项使用不同的Trotter步骤。我们用来限制模拟给定分子的复杂性的方法是有效的，与依赖于指数代价的经典精确模拟的[1，2]的方法相反。
The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies [1, 2] have cast a shadow on this hope by revealing that the complexity in gate count of such simulations increases with the number of spin orbitals N as N8, which becomes prohibitive even for molecules of modest size N ∼ 100. This study was partly based on a scaling analysis of the Trotter step required for an ensemble of random artificial molecules. Here, we revisit this analysis and find instead that the scaling is closer to N6 in worst case for real model molecules we have studied, indicating that the random ensemble fails to accurately capture the statistical properties of real-world molecules. Actual scaling may be significantly better than this due to averaging effects. We then present an alternative simulation scheme and show that it can sometimes outperform existing schemes, but that this possibility depends crucially on the details of the simulated molecule. We obtain further improvements using a version of the coalescing scheme of [1]; this scheme is based on using different Trotter steps for different terms. The method we use to bound the complexity of simulating a given molecule is efficient, in contrast to the approach of [1, 2] which relied on exponentially costly classical exact simulation.