论文标题
与矢量规范缩放的时间有关的无界哈密顿模拟
Time-dependent unbounded Hamiltonian simulation with vector norm scaling
论文作者
论文摘要
量子动力学仿真的准确性通常是通过统一运算符规范中单位进化算子的误差来衡量的，这又取决于哈密顿量的某些规范。对于无限的运营商，在适当的离散化之后，哈密顿量的规范可能非常大，这大大增加了模拟成本。但是，操作员规范测量了量子模拟的最坏情况误差，而实际模拟涉及有关当前给定初始向量的误差。我们证明，在哈密顿量和初始矢量的合适假设下，如果根据向量规范来衡量误差，则随着使用猪肉手类型方法的增加，计算成本可能根本不会增加。从这个意义上讲，我们的结果优于量子模拟文献中所有以前的错误界限。我们的结果扩展了[Jahnke，Lubich，Bit Numer。数学。 2000]到时间依赖的设置。我们还阐明了trotter和广义猪猪的换向量表对于时间依赖的汉密尔顿模拟的存在和重要性。
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discretization, the norm of the Hamiltonian can be very large, which significantly increases the simulation cost. However, the operator norm measures the worst-case error of the quantum simulation, while practical simulation concerns the error with respect to a given initial vector at hand. We demonstrate that under suitable assumptions of the Hamiltonian and the initial vector, if the error is measured in terms of the vector norm, the computational cost may not increase at all as the norm of the Hamiltonian increases using Trotter type methods. In this sense, our result outperforms all previous error bounds in the quantum simulation literature. Our result extends that of [Jahnke, Lubich, BIT Numer. Math. 2000] to the time-dependent setting. We also clarify the existence and the importance of commutator scalings of Trotter and generalized Trotter methods for time-dependent Hamiltonian simulations.
