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Work conducted with the group of Serge Haroche, Physics Nobel Prize 2012.  

Collaboration began in the autumn of 2009 with the cavity quantum electrodynamics group at   the Laboratoire Kastler-Brossel (LKB) of  the ENS - Paris,  group  led  by  Serge Haroche (Physics  Nobel Prize 2012) and  Jean-Michel Raimond.

Mazyar Mirrahimi from INRIA, and Pierre Rouchon from MINES ParisTech, contributed to the development of a control algorithm used for the first experimental implementation of a quantum feedback loop. It was the first time that a full quantum state, involving not only the populations but also the coherences, was computed in real-time and exploited in a feedback loop.

The control goal consists in stabilizing light around photon-number states (Fock states). These quantum states are very different from classical ones describing usual light: they are fragile, difficult to generate and to stabilize. The interest, but also the difficulty of this experiment, lie in the fact that the measurement process, present in any feedback loop, induces unavoidable random perturbations on the system to be controlled. The feedback algorithm used for this experiment relies on a quantum adaptation of Lyapunov control techniques. The "Centre Automatique et Systèmes" of MINES ParisTech with the key contributions of Laurent Praly, has, for many years, developed these control techniques that are very efficient for classical systems. This quantum feedback experiment, which was published in the 1 September 2011 issue of Nature, can be seen as a significant step  towards the quantum computer. Protection via feedback of quantum states could be an efficient method to fight against decoherence, the random and devastating perturbations due to the environment, perturbations which, currently, are the major obstacles to overcome. In this experiment, the controller and actuator are classical devices whereas the system and its measurement are quantum devices. This kind of feedback is called a measurement-based feedback.  

Collaboration with the cavity quantum electrodynamics group of LKB have continued until now with joint publications on another kind of feedback that directly exploits the back-action due to the measurement process.  Such feedback schemes, related to reservoir engineering, are also called coherent feedback. They are characterized by the fact that the controller and the actuator are also quantum devices: they are subject to irreversible and dissipative processes whose stabilizing influences are transmitted via an adapted coupling to the system to be controlled.  Coherent feedback can be seen as an extension of the optical pumping methods introduced by Alfred Kastler (Physics Nobel Prize 1966) and widely used nowadays.   

Thus, it is possible, via a coherent feedback and with a realistic experimental setup, to stabilize and to protect Schrödinger cat-states against decoherence. These quantum states are crucial to investigate the frontier between classical and quantum worlds. These states are built with classical states (the cat is dry, the cat is wet...) and their quantum features rely on the notion of coherent superposition, a notion that has no classical equivalent. These states could have possible applications for coding and manipulating quantum information. The phase cat-states of an harmonic oscillator, as the cat-state of the figure, are not instantaneously destroyed  by the decoherence:  they benefit from the robustness of their  constitutive classical states.   

QUANTIC Project on quantum circuits

The models developed for cavity quantum electrodynamics can be directly applied to quantum circuits. These circuits have made substantial experimental progress during the last decade. The QUANTIC Project proposes to apply and develop the control methods presented above. QUANTIC is thus a project which brings together physicists specializing in quantum circuits and mathematicians specializing in control theory.  The physicists are Benjamin Huard and François Mallet. They conduct, in the Laboratoire Pierre Aigrain of the ENS Paris, experiments on integrated quantum circuits. The mathematicians are Mazyar Mirrahimi from INRIA and Pierre Rouchon from MINES ParisTech.

One of the goals of the QUANTIC Project is to construct a memory  that can:  

  • catch a  quantum state propagating on a transmission line; 
  • store and protect  this  state for a long time;    
  • release this state on another transmission line and make it available for future manipulations.

Such quantum memory is a key component of a quantum computer.

A second goal consists in generating and protecting entangled states that are spatially delocalized. Such delocalized entangled states are crucial for teleportation. They are also key resources for quantum repeaters in long-distance quantum communications.  

A third goal consists in designing circuits that conduct elementary quantum operations and that are fault tolerant. This last goal requires generalizing coherent feedback to stabilize not only quantum states but also quantum operations.

Mathematical system theory redesigned for the quantum world

These practical, experimental goals will provide an opportunity to adapt and probably redesign the mathematical theory of classical systems to take into account quantum specificities. This theory which expanded significantly since the mid 20th century, with the development of radar, telecommunications and digital computers, underlies numerous current technological achievements. The QUANTIC project will contribute to devising a quantum extension of this theory, around the key concepts of feedback, stability and robustness.