Talks

Eukaryotic cells and bacteria can use the substrate to self-regulate their movement. Eukaryotic cells, such as MDCK epithelial cells, leave footprints on the substrate, which are then used to regulate their motility and exploratory behavior. On the other hand, Escherichia coli bacteria stop and adhere to the surface to break confinement when swimming close to the surface and explore their surroundings more efficiently. In this talk, I will explore these mechanisms through mathematical models highlighting how both cells and bacteria, at two different biological scales, use the environment to self-regulate the way they explore their surroundings.

The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. We complement our analytical findings with numerical experiments that showcase that, in certain situations, noise can increase the expressivity of parametrized quantum circuits.