"Discrete-time, discrete-space quantum theory"
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Physics usually formulates its laws in the language of Partial
Differential Equations. But in order to solve these equations PDEs numerically,
we usually have to discretize both time and space, thereby obtaining a discrete
numerical model of the physical phenomenon that we are interested in. The broad
category of computer models that are obtained in this way is called Cellular
Automata. Thus, it could be said that we end up formulating physics phenomena in
the language of computer programs. 
In this talk, we will see how much of that can be done with Quantum Physics. We
will mention results about: the mathematical structure of discrete time discrete
space models of quantum theory; the notion of simulation in those Quantum
Cellular Automata; how to formulate some quantum physics phenomenon in the
language of quantum computers programs.