论文标题
线性量子随机系统的二次指数功能率的状态空间计算
State-space computation of quadratic-exponential functional rates for linear quantum stochastic systems
论文作者
论文摘要
本文涉及由多通道玻色子场驱动的线性量子随机系统的二次指数函数（QEF）的无限 - 摩托子生长速率。这种对风险敏感的性能标准对系统变量的二次功能的积分施加了指数罚款，其最小化可提高系统的鲁棒性在量子统计不确定性方面，并使其行为在尾部分布方面更加保守。我们使用带有真空输入字段的系统中不变的高斯量子状态的QEF增长率的频域表示，以便在状态空间中计算它。 QEF速率与无限线性系统级联产生的经典固定高斯随机过程的类似功能有关。这种塑形过滤器的截断可以通过求解代数Lyapunov方程的复发序列以及代数riccati方程来以任何精度计算QEF速率。 QEF速率的状态空间计算及其与频域结果的比较通过一个开放量子谐波振荡器的数值示例证明。
This paper is concerned with infinite-horizon growth rates of quadratic-exponential functionals (QEFs) for linear quantum stochastic systems driven by multichannel bosonic fields. Such risk-sensitive performance criteria impose an exponential penalty on the integral of a quadratic function of the system variables, and their minimization improves robustness properties of the system with respect to quantum statistical uncertainties and makes its behaviour more conservative in terms of tail distributions. We use a frequency-domain representation of the QEF growth rate for the invariant Gaussian quantum state of the system with vacuum input fields in order to compute it in state space. The QEF rate is related to a similar functional for a classical stationary Gaussian random process generated by an infinite cascade of linear systems. A truncation of this shaping filter allows the QEF rate to be computed with any accuracy by solving a recurrent sequence of algebraic Lyapunov equations together with an algebraic Riccati equation. The state-space computation of the QEF rate and its comparison with the frequency-domain results are demonstrated by a numerical example for an open quantum harmonic oscillator.
