Many of you will have played with cellular automata such as Conway's Game of Life. These are model systems in which complex and chaotic behaviors emerge from simple dynamical rules.

Motivated by quantum computation, physicists have in recent years begun to study quantum circuits, which are in some way a quantum analogue of cellular automata. In this talk, I'll discuss some of the similarities and differences between these two classes of systems, and what they can teach us about classical and quantum dynamics more generally.

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