Quantum Cellular Automata over discrete groups

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• Paolo Boldrini (Chalmers University of Technology)
• Thursday 03 July 2025, 11:55-12:00
• External.

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TGAW01 - Crossed products and groupoid C*-algebras

Given a finite set $k$ and a countable discrete group $G$, a cellular automaton is a continuous map from $k^{G$ to itself which is equivariant with respect to the Bernoulli shift. In this lightning talk, I will explore a noncommutative analogue of this concept, where the finite set $k$ is replaced by a finite-dimensional C-algebra and the Cartesian product $k}G$ is replaced by an infinite tensor product. These objects, known as quantum cellular automata, were introduced by Schumacher and Werner, with a primary focus on the case of integer actions and simple finite dimensional C-algebras. I will present generalizations of some of their results to more general groups, and discuss some questions that arise in this broader context.

This talk is part of the Isaac Newton Institute Seminar Series series.

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