A quantum extended Kalman filter
A quantum extended Kalman filter
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DOI：
10.1088/1751-8121/aa6e5e
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
M. Emzir;M. Woolley;I. Petersen
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文献类型：
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作者：
M. Emzir;M. Woolley;I. Petersen
在量子物理学中，随机主方程（SME）根据对系统的测量记录估计Schrödinger图像中量子系统的状态（密度算子）。在海森堡的图像中，SME是一个量子滤波器。对于一个受线性测量和高斯噪声影响的线性量子系统，其动力学可以用量子随机微分方程（QSDEs）来描述，也称为量子朗之万方程，而量子滤波器则简化为所谓的量子卡尔曼滤波器。在本文中，我们介绍了一种量子扩展卡尔曼滤波器（quantum extended Kalman filter, quantum EKF），它将交换逼近和时变线性化应用于非线性QSDEs系统。我们将证明，在某些条件下，类似于经典EKF的滤波器可以用于量子系统。讨论了估计误差的有界性以及过程噪声和测量噪声的状态相关协方差滤波问题。我们通过将量子EKF应用于涉及多模、非线性哈密顿量和同时跳跃扩散测量的系统来证明它的有效性。
In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.