Related papers: Approximation of diffeomorphisms for quantum state transfers

Approximation of diffeomorphisms for quantum state transfers

URL: http://arxiv.org/abs/2503.14450v1
Date: Tue, 18 Mar 2025 17:28:59 GMT
Title: Approximation of diffeomorphisms for quantum state transfers
Authors: Eugenio Pozzoli, Alessandro Scagliotti,
Abstract summary: We seek to combine two emerging standpoints in control theory.<n>We numerically find control laws driving state transitions in a bilinear Schr"odinger PDE posed on the torus.
Score: 49.1574468325115
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this paper, we seek to combine two emerging standpoints in control theory. On the one hand, recent advances in infinite-dimensional geometric control have unlocked a method for controlling (with arbitrary precision and in arbitrarily small times) state transfers for bilinear Schr\"odinger PDEs posed on a Riemannian manifold $M$. In particular, these arguments rely on controllability results in the group of the diffeomorphisms of $M$. On the other hand, using tools of $\Gamma$-convergence, it has been proved that we can phrase the retrieve of a diffeomorphism of $M$ as an ensemble optimal control problem. More precisely, this is done by employing a control-affine system for \emph{simultaneously} steering a finite swarm of points towards the respective targets. Here we blend these two theoretical approaches and numerically find control laws driving state transitions (such as eigenstate transfers) in a bilinear Schr\"{o}dinger PDE posed on the torus. Such systems have experimental relevance and are currently used to model rotational dynamics of molecules, and cold atoms trapped in periodic optical lattices.

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