论文标题
哈密顿量和单位产品的总和的确切对角线化
Exact Diagonalization of Sums of Hamiltonians and Products of Unitaries
论文作者
论文摘要
我们提供了广泛适用的工具，用于在添加自偶会操作员以及在有限维的希尔伯特空间中确定特征值和特征向量的行为。新工具为特征值和特征向量提供了明确的非扰动表达式。为了说明新工具的广泛适用性，我们概述了一些应用程序在信息理论中进行抽样。更长的伴侣论文将新工具应用于绝热的量子演化，从而为绝热量子计算对纠缠资源的用法与量子计算的速度的使用之间的联系散发出了新的启示。
We present broadly applicable tools for determining the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitaries, in finite-dimensional Hilbert spaces. The new tools provide explicit non-perturbative expressions for the eigenvalues and eigenvectors. To illustrate the broad applicability of the new tools, we outline several applications, for example, to Shannon sampling in information theory. A longer companion paper applies the new tools to adiabatic quantum evolution, thereby shedding new light on the connection between an adiabatic quantum computation's usage of the resource of entanglement and the quantum computation's speed.
