无限维量子系统的有限能控性
Finite Controllability of Infinite-Dimensional Quantum Systems
摘要：
与计算和通信应用有关的量子现象几乎总是涉及本征态之间的特定转移及其线性叠加。对于某些量子系统，如自旋系统，量子演化方程（薛定谔方程）是有限维的，并且在李群和商空间上定义的系统的可控性的旧结果提供了大部分所需的非耗散系统的可控性。然而，在无限维的环境中，控制量子系统的演化往往存在概念和技术上的困难。在本文中，我们提出了一个系统的方法来解决一类这样的问题，它是可以避免一些技术问题。特别是，我们分析了无限维双线性系统的可控性的假设下，使可控性可能使用的轨迹躺在一个嵌套的家庭预定义的子空间。这个结果，我们称之为有限可控性定理，提供了一组在无限维设置可控性的充分条件。我们考虑特定的物理系统，感兴趣的量子计算，并提供洞察类型的量子操作（门），可能会被开发。
英文摘要：
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schrödinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
