Bremen 2017 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Quantum Information and Thermodynamics

MP 2.3: Talk

Monday, March 13, 2017, 15:15–15:35, SFG 2010

A geometric viewpoint on quantum control — •Davide Pastorello — University of Trento and TIFPA, Trento

Quantum mechanics can be geometrically formulated in a symplectic fashion on the projective space (as a Kähler manifold) constructed out from the Hilbert space of the considered quantum theory. Within such a framework quantum dynamics can be represented by the flow of a Hamiltonian vector field in analogy to classical mechanics.

In this talk I propose a new geometric approach to controllability of a n-level quantum system from the viewpoint of geometric structures, exploiting some tools of classical control theory. In particular the notion of the accessibility algebra of classical non-linear systems in affine form can be adapted to study quantum controllability within geometric Hamiltonian formulation of quantum mechanics. Moreover the controllability of a quantum system can be completely characterized in terms of Killing vector fields on the complex projective space w.r.t. Fubini-Study metric.

The talk is mainly based on the following paper: D. Pastorello, A geometric approach to quantum control in projective Hilbert spaces. Accepted for publication in Reports in Mathematical Physics (2016).