2012/02/05 by Vladimirov, Igor G., Petersen, Ian R. · 1 citation
#81S22 #81S25 #81S30 #93B18 #93B28 #93E24 #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #Probability (math.PR) #Quantum Physics (quant-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1202.0946
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable to the design of suboptimal controllers and filters for nonlinear quantum systems.