# Are there any proved consistent quantum continuous cellular automata/game of life model?

There are quantum cellular automata (continuous game of life, which is a type of cellular automata): https://hal.archives-ouvertes.fr/hal-00542373/document

There are continuous cellular automata (continuous game of life which is a type of cellular automata) https://arxiv.org/abs/1111.1567

But I have not seen any quantum continuous cellular automata.

I found a paper (https://arxiv.org/abs/1701.02252) that says that with a Hamiltonian cellular automaton there can be a map between cellular automaton and quantum continuous, but a user in this site, told me that it was not really continuous because time was discrete even in a continuous universe in that model

I also found this paper: https://arxiv.org/abs/1606.08764

There, it is said "We realize constant-space quantum computation by measure-many two-way quantum finite automata" I don't know if that means that this model is a quantum continuous (in space, time...etc) cellular automata/game of life

So do you know of any model that would satisfy what I ask?

• I don’t think this is quite the right question to ask. If you define a cellular automaton as anything with discrete time and discrete space and fixed update rules, then obviously anything can be written as a cellular automaton. This is kind of like how almost every numerical simulation ever works. It’s just like how you could write any program in assembly if you really wanted to. – knzhou Jun 27 '18 at 11:58
• However, the fact that you can write physical laws in terms of cellular automata doesn’t mean you should. It seems to be an extremely clunky and inefficient rewriting of something we already know. – knzhou Jun 27 '18 at 12:00
• @knzhou why is it clunky and inefficient? – user199226 Jun 29 '18 at 14:37
• @knzhou except there are provably numbers we can't compute, so it's not obvious to me that anything can be written that way? – CDCM Jun 29 '18 at 15:08
• @CDCM No, that's a mathematician's way of viewing things. Such numbers don't matter for physics. For the purposes of physics you could even postulate that all numbers are multiples of $10^{-100}$. Nothing will go wrong, because we cannot measure nearly that precisely anyway. – knzhou Jun 29 '18 at 15:14