7 research outputs found
Lyapunov Stability Analysis for Invariant States of Quantum Systems
In this article, we propose a Lyapunov stability approach to analyze the
convergence of the density operator of a quantum system. In contrast to many
previously studied convergence analysis methods for invariant density operators
which use weak convergence, in this article we analyze the convergence of
density operators by considering the set of density operators as a subset of
Banach space. We show that the set of invariant density operators is both
closed and convex, which implies the impossibility of having multiple isolated
invariant density operators. We then show how to analyze the stability of this
set via a candidate Lyapunov operator.Comment: A version of this paper has been accepted at 56th IEEE Conference on
Decision and Control 201
A quantum extended Kalman filter
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