Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
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DOI：
10.3390/e21121218
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发表时间：
2019-12-13
期刊：
影响因子：
2.7
通讯作者：
Coveney PV
中科院分区：
文献类型：
--
作者：
Tranter A;Love PJ;Mintert F;Wiebe N;Coveney PV
Trotter – Suzuki分解经常用于量子化学的量子模拟中。数字。通过替代手段，由于可能相对于术语数量的阶乘数量，trot脚的误差取决于应用单个单位的顺序。在本文中，我们提出了三种订购策略，并评估其对猪肉误差的影响。在STO-3G的基础上，我们证明了最佳订购方案如何取决于汉密尔顿的兼容性图，并显示其随着键长的长度而变化。考虑到所获得的颜色的属性。 Kcal/mol相对于此而言，订购方案之间的差异大约是在毫毛的顺序上。最后，我们考虑基于托特特错误操作员的规范订购策略，包括一种迭代方法将一个术语插入一个有序的哈密顿人。
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.
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