https://hal-mines-paristech.archives-ouvertes.fr/hal-00971498Silveira, H.B.H.B.SilveiraLaboratory of Automation and Control, Department of Telecommunications and Control Engineering - USP - University of São PauloPereira da Silva, P.S.P.S.Pereira da SilvaDepartment of Telecommunications and Control Engineering - USP - Universidade de São PauloRouchon, PierrePierreRouchonCAS - Centre Automatique et Systèmes - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresA stochastic Lyapunov feedback technique for propagator generation of quantum systems on U(n)HAL CCSD2013[SPI.AUTO] Engineering Sciences [physics]/AutomaticChaplais, François2014-04-02 23:23:122021-11-17 12:30:582014-04-02 23:23:12enConference papers1This work treats the problem of generating any desired goal propagator for a driftless quantum system that evolves on the unitary group U(n). The physical relevance of such control problem is the realization of arbitrary quantum gates in quantum computers. Assuming only the controllability of the system, the paper constructs explicit stochastic control laws that assure global asymptotic convergence of the propagator of the system towards the goal propagator. The purpose of introducing a stochastic behaviour in the controls is to speed up convergence. The control strategy can be rigorously proved based on Lyapunov feedback and stochastic techniques. The controls laws rely on a reference trajectory that crosses the desired goal propagator in a time-periodic fashion and such that its corresponding linearised system generates the Lie algebra u(n). Their existence is ensured by the ReturnMethod of Coron, and standard Fourier series results allows them to be explicitly constructed.