论文标题
克服指数缩放，并在受约束的哈密顿人的trotter-suzuki实现中使用系统大小：2+1 U（1）晶格量规理论
Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories
论文作者
论文摘要
对于许多感兴趣的量子系统，模拟其时间演变量表的经典计算成本在系统大小上成倍增加。同时，已经证明量子计算机可以使用与系统大小多个缩放的资源对其中一些系统进行模拟。鉴于使用量子计算机用于使用经典设备不可行的模拟潜力，因此至关重要的是，人们仔细研究量子算法的缩放。这项工作确定了一系列受约束系统的哈密顿式术语，这些术语是天真地需要在系统大小上成倍扩展的量子资源。一个重要的例子是在具有周期性边界条件的晶格上的紧凑型u（1）量规理论。施加磁性高斯定律，先验地将限制引入了该哈密顿量，这是天真地导致指数深的回路。然后开发了一种方法，该方法使用操作员的重新定义将这种缩放量化为系统大小的多项式。给出了定义运算符基础变化的矩阵的明确结构，以及相关计算成本的缩放。
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these systems using resources that scale polynomially with the system size. Given the potential for using quantum computers for simulations that are not feasible using classical devices, it is paramount that one studies the scaling of quantum algorithms carefully. This work identifies a term in the Hamiltonian of a class of constrained systems that naively requires quantum resources that scale exponentially in the system size. An important example is a compact U(1) gauge theory on lattices with periodic boundary conditions. Imposing the magnetic Gauss' law a priori introduces a constraint into that Hamiltonian that naively results in an exponentially deep circuit. A method is then developed that reduces this scaling to polynomial in the system size, using a redefinition of the operator basis. An explicit construction of the matrices defining the change of operator basis, as well as the scaling of the associated computational cost, is given.
