基于正则QR分解的稳定离散量子动力学
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
摘要：
我们分析了离散时间，马尔可夫量子系统的渐近行为相对于一个子空间的兴趣。子空间的全局渐近稳定性与量子信息处理有关，特别是对于在纯态或子空间码中初始化系统。我们提供了一个线性代数表征的动力学性质，导致一个给定的量子子空间的不变性和吸引性。然后，我们构造了一个离散时间反馈控制的设计算法，允许稳定的目标子空间，证明如果控制问题是可行的，那么该算法返回一个有效的控制选择。为了证明这一结果，一个典型的QR矩阵分解推导出来，也被用来建立控制方案的潜力，开放系统动力学的仿真。
英文摘要：
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.
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