We will prove the existence of a universal quantum cellular automaton. Such qca are defined as the quantum-mechanical pendant of classical one-dimensional cellular automata. As is the case with quantum Turing machines, the well-formedness restriction plays an important role. It will be shown that every proper qca obeys a local constraint which is comparable with the ‘inverse neighborhood’ of cl...

A class of fermionic quantum field theories with interactions is shown to be equivalent probabilistic cellular automata, namely automata a probability distribution for the initial states. Probabilistic on one-dimensional lattice are two-dimensional fermions. They can viewed as generalized Ising models square and therefore classical statistical systems. As they Thus mechanics emerges from statis...