Thank you for a quick answer! I'll take a look at it, my curiosity
approves additional items on my TODO list :-)
> The classical universal
> dovetailer generates easily all the quantum computations, but I find
> hard to just define *one* unitary transformation, without measurement,
> capable of generating forever greater computational memory space. Other
> problems are more technical, and are related to the very notion of
> universality and are rather well discussed in the 2007 paper:
> Deutsch's Universal Quantum Turing Machine revisited.
> I could relate this with technical problem with the BCI combinator
> algebra, that is those structure in which every process are reversible,
> and no cloning are possible (cf the No Kestrel, No Starling summary of
> physics(*)). Those algebra are easily shown being non turing universal,
> and pure unitarity seems to me to lead to such algebra.
> Could you implement with a quantum computer the "really infinite"
> counting algorithm by a purely unitary transformation? The one which
> generates without stopping 0, 1, 2, 3, ... That would already be a big help.
> (*) Marchal B., 2005, Theoretical computer science and the natural
> Physics of Life Reviews, Vol. 2 Issue 4 December 2005, pp. 251-289.
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