Global stability criterion for a quantum feedback control process on a single qubit and exponential stability in case of perfect detection efficiency

Abstract

Quantum feedback control is a technology which can be used to drive a quantum system into a predetermined eigenstate. In this article, sufficient conditions for the experiment parameters of a quantum feedback control process of a homodyne QND measurement are given to guarantee feedback control of a spin-1/2 quantum system in case of imperfect detection efficiency. For the case of pure states and perfect detection efficiency, time scales of feedback control processes are calculated.

Optimal control equation for quantum stochastic differential equations

“…Within this set-up, several classical stochastic control methods such as optimal control [13][14][15] or Lyapunov stabilization [16][17][18][19] had been designed. In figure5, we proposed a possible experimental set-up for nonlinear optical quantum feedback control of atomic observables.…”

“…J Quantum trajectories are classical Itô stochastic differential equations for the so-called density matrix of quantum system; and hence the classical stochastic control theory can be developed for them. For instance, Hamilton-JacobiBellman (HJB) equation and separation principle [13][14][15] and Lyapunov stability theory [16][17][18][19] were developed for quantum filtering equations.…”