Semi-Algebraic Problem Approach for Design of Quantum Spin Control Systems in the Face of Feedback Delay

Abstract

Accurate control of quantum spin is necessary in order to utilize quantum spin as the physical realization of the quantum bit. Feedback control (based on continuous quantum measurement) of quantum spin systems inevitably suffers from estimation delays. In this paper, we state that a control system which takes into account these delays can be described by using stochastic delay differential systems. Moreover, we can restrict our analysis to the class of systems which have polynomial coefficients and evolve in a bounded semi-algebraic set. Then, the problem of stabilizing such systems is shown to be solvable effectively via reduction to a semi-algebraic problem.