论文标题
数字绝热量子模拟量子$ \ mathbb {z} _2 $ lattice量规理论
Trotter errors in digital adiabatic quantum simulation of quantum $\mathbb{Z}_2$ lattice gauge theory
论文作者
论文摘要
猪肉分解是数字量子模拟的基础。在我们的GPU演示中，使用了不对称和对称分解，用于$ 2+1 $ dimensional Quantum $ \ Mathbb {Z} _2 $ lattice Gauge理论的数字绝热量子模拟。研究了铲子分解中的实际误差，作为耦合参数的函数，以及耦合参数变化的每个步骤中的猪肉取代的数量。能量的相对误差显示与通常根据进化运算符定义的猪根误差密切相关。它们远小于稳定顺序的估计。对称分解的误差远小于非对称分解中的误差。此处获得的践踏误差的特征可用于实验数字量子模拟及其数值演示的实现。
Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of $2+1$ dimensional quantum $\mathbb{Z}_2$ lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be closely related to the Trotter error usually defined defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.
