Mathematics

Over the years, numerous mathematical aspects related to quantum engineering at large have become topics of research for mathematicians and mathematical physicists interested in the recent developments of quantum mechanics.
This is certainly due to the fact that today’s experimental capacities in this field are able to test fundamental questions that admit clear and simple enough mathematical formulations. Also, many applications of quantum ideas to scientific fields ranging from quantum information theory to the design of actual computational devices, together with their quantum algorithms, reveal new and interesting mathematical challenges.

Popular topics of mathematical research associated with aspects of quantum engineering concern for example:

  • conceptual aspects of quantum statistical mechanics, in and out of equilibrium, for deterministic and random models,
  • statistical properties of quantum measurement procedures, quantum hypotheses testing procedures, quantum correlations in various conditions,
  • dynamics of decoherence and/or intrication of general open quantum systems,
  • energy/entropy costs of information encoding and retrieval quantum protocols,
  • effective quantum dynamics, Markovian of not, continuous or discrete in time, and associated models, such as quantum walks,
  • quantum control, with or without feedback, of various systems in several regimes,
  • ...

As a witness of this activity at the international level, note the presence of sessions specifically dedicated to quantum information at the triennal meeting of the “International Association of Mathematical Physics” and at other high profile generalist conferences in mathematical physics, such as the “Qmath” or “Spectral Days” series, for almost a decade.

At the national level, the GDR DynQua coordinates the activities in the field mathematical physics. A large part of the research lead by its members concerns some of the topics listed above, or their ramifications.

On the Grenoble campus, the Institut Fourier, and to a lesser extent the Laboratoire Jean Kuntzmann, hosts mathematicians working on certain topics related to quantum engineering. In particular, the team “physique mathématique” of the Institut Fourier concentrates expertise on the dynamics of open quantum systems, spectral and semi-classical analysis, quantum dynamics in random media, geometry of intrication, quantum optics, aspects of quantum information.

The goals pursued by the program Quantum Engineering will require joint efforts of the different scientific communities present on the Grenoble Campus. With that respect, several mathematica physicists have a proven a record of successful and on-going collaborations with theoretical physicists, which we intend to intensify.