论文标题
相互作用的电子几乎紧密
Nearly tight Trotterization of interacting electrons
论文作者
论文摘要
我们考虑在数字量子计算机上模拟量子系统。我们表明，可以通过同时利用目标汉密尔顿的交换性，相互作用的稀疏以及初始状态的先验知识来提高量子模拟的性能。我们使用Trotterization对一类相互作用的电子进行了Trotterization，该电子涵盖了各种物理系统，包括平面波 - 基本电子结构和费米 - 哈伯德模型。我们通过在$η$ -Electron歧管内采取嵌套换向器的过渡幅度来估计模拟误差。我们开发了多种技术，以界定一般费米子操作员的过渡幅度和期望，这可能具有独立的利益。我们表明，使用$ \ left（\ frac {n^{5/3}}} {η^{2/3}}+n^{4/3} {4/3}η^{2/3} \ {2/3} \ right）当$ n =η^{2-o（1）} $时，量化为可忽略的因素，同时胜过首次量化的仿真。我们还获得了模拟费米 - 哈伯德模型的改进。我们构建了混凝土示例，其边界几乎饱和，从而几乎对相互作用的电子进行了紧密的to。
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the $η$-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use $\left(\frac{n^{5/3}}{η^{2/3}}+n^{4/3}η^{2/3}\right)n^{o(1)}$ gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $η$ electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when $n=η^{2-o(1)}$. We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.
