Propagator Generation of Quantum Systems
Event details
| Date | 29.04.2013 |
| Hour | 14:15 › 15:15 |
| Speaker | Paulo Sergio Pereira da Silva |
| Location |
ME C2 405
|
| Category | Conferences - Seminars |
This work treats the problem of generating any desired goal
propagator for a driftless quantum system that evolves on the special
unitary group SU(n) (or 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 presentation
constructs explicit control laws that assure global asymptotic
convergence of the propagator of the system towards the goal
propagator. 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 su(n) (or u(n)). Their existence is ensured by the Return
Method of Coron. The stability of the tracking of the reference
trajectory is assured by a convenient Application of a version LaSalle's
Invariance Theorem [1]. The efficience of the control law can be improved
when one combines this control law with a random selection of some
control parameters. In this case, the closed loop stability can be shown
as an application of Kushner's Theorem (a stochastic version of Lassale's
Invariance Theorem) [2].
[1] H. Bessa Silveira, P. S. Pereira da Silva, an P. Rouchon.
Explicit Control Laws for the Periodic Motion Planning of Controllable
Driftless Systems on SU(n). IEEE Conference on Decision and Control
CDC'2012. p. 3640-3645.
[2] H. Bessa Silveira, P. S. Pereira da Silva, an P. Rouchon.
A Stochastic Lyapunov Feedback Technique for Propagator Generation of
Quantum Systems on U(n). Submitted to ECC'2013.
Authors: Hector Bessa Silveira, Paulo Sergio Pereira da Silva and Pierre Rouchon.
propagator for a driftless quantum system that evolves on the special
unitary group SU(n) (or 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 presentation
constructs explicit control laws that assure global asymptotic
convergence of the propagator of the system towards the goal
propagator. 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 su(n) (or u(n)). Their existence is ensured by the Return
Method of Coron. The stability of the tracking of the reference
trajectory is assured by a convenient Application of a version LaSalle's
Invariance Theorem [1]. The efficience of the control law can be improved
when one combines this control law with a random selection of some
control parameters. In this case, the closed loop stability can be shown
as an application of Kushner's Theorem (a stochastic version of Lassale's
Invariance Theorem) [2].
[1] H. Bessa Silveira, P. S. Pereira da Silva, an P. Rouchon.
Explicit Control Laws for the Periodic Motion Planning of Controllable
Driftless Systems on SU(n). IEEE Conference on Decision and Control
CDC'2012. p. 3640-3645.
[2] H. Bessa Silveira, P. S. Pereira da Silva, an P. Rouchon.
A Stochastic Lyapunov Feedback Technique for Propagator Generation of
Quantum Systems on U(n). Submitted to ECC'2013.
Authors: Hector Bessa Silveira, Paulo Sergio Pereira da Silva and Pierre Rouchon.
Practical information
- General public
- Free
Organizer
- Muellhaupt Philippe