Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
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DOI：
10.1021/acs.jctc.9b01083
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发表时间：
2020-01-01
影响因子：
5.5
通讯作者：
Mayhall, Nicholas J.
中科院分区：
文献类型：
--
作者：
Grimsley, Harper R.;Claudino, Daniel;Mayhall, Nicholas J.
变分量子本征求解器（VQE）已成为近期最有前途的量子算法之一，可用于模拟分子电子结构等多体系统。作为 VQE 算法中一个有吸引力的模拟，酉耦合簇 (UCC) 理论在最近的文献中重新引起了人们的兴趣。然而，与最初的经典 UCC 理论不同，量子计算机上的实现需要有限阶 Suzuki-Trotter 分解来分离泡利算子大和的指数。虽然以前的文献已经认识到 UCC 方法的 Trotterized 形式中算子的不同排序的非唯一性，但不同排序在化学尺度上是否重要的问题尚未得到解决。在这封信中，我们探讨了算子排序对 Trotterized UCCSD ansatz 以及 Lee 等人最近提出的更紧凑的 k-UpCCGSD ansatz 的影响。 [J.化学。理论计算, 2019, 15, 311. arXiv, 2019, quant-ph:1909.09114. https://arxiv.org/abs/1909.09114]。我们观察到不同算子排序的 Trotterizations 能量存在显着的、系统相关的变化。能量变化发生在化学尺度上，有时约为数百千卡/摩尔。这封信不仅需要定义 ansatz 中存在的操作符，还需要定义它们出现的顺序。除了科学再现性的普遍重要性之外，这对于遵守“模型化学”的量子化学概念也是必要的。最后一点，我们建议一种有用的策略，从可能性的组合数量中选择一个定义明确且有效的运算符排序。
The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the nonuniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this Letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. [ J. Chem. Theory Comput., 2019, 15, 311. arXiv, 2019, quant-ph:1909.09114. https://arxiv.org/abs/1909.09114]. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This Letter establishes the need to define not only the operators present in the ansatz but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a "model chemistry", in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.