Descriptif

This course is destined to applied mathematics and physics students with interest in quantum information and computation. The course subject is the mathematical modelling of devices that enable us to manipulate the quantum state of light and matter in the aim of realizing a quantum processor. While the developed methodology is applicable to various hardware problems in recently developed quantum technologies, the quantum software problems (e.g. quantum algorithms) are not initiated in this course.

One of the most needed requirements for any operating quantum machine is to prepare various non-classical states with high fidelities, manipulate them reliably and protect them over arbitrary long times. In manipulating such quantum systems, one needs to take into account various experimental uncertainties and the destructive effects of the coupling to an uncontrolled environment leading to the loss of coherence in quantum information. On the other hand, in order to protect (against decoherence) the quantum information carried by such a system, one needs to intentionally couple the system to an environment either to measure some physical observables (in an active measurement-based feedback scheme) or to evacuate the entropy (in a passive dissipation engineering scheme).

This course focuses on dynamical models (ordinary and partial differential equations, discrete and continuous-time stochastic systems) behind such quantum systems and control tools allowing the manipulation and stabilization of some interesting non-classical states. By focusing on the particular case of a qubit (two-level quantum system) coupled to a harmonic oscillator, we will present open-loop control tools (pulse shaping techniques) that are robust to experimental systematic errors and stochastic time-dependent noise. We will also introduce and analyze various dynamical models for open quantum systems undergoing repetitive or continuous measurements, and will study their stabilization through closed-loop control techniques (feedback).