**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Fri, 10 Sep 1999 13:03:18 +0300 (EET DST)*

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Dear All,

A note about quantum computing. The basic enemy quantum computer builders

encounter is decoherence. What happens is that

entangled subsystem tends to generate entanglement with surroundings.

In standard physics this phenomenon makes selves impossible:

even slightest entanglement generated by time development U during

quantum jump Psi_i-->UPsi_i-->Psi_f would kill self and selves

would be desperaly nongeneric phenomenon: single self, if it

managed to wake-up, would die during next quantum jump.

The solution to the problem is provided by p-adicity. Self is system

able to remain *p-adically* unentangled. This means that subsystem

able to stay self develops subcritical real entanglement in each quantum

jump: this corresponds to vanishing p-adic entanglement entropy

defined to be p-adic entanglement entropy with pinary cutoff. Pinary

cutoff is uniquely determined by the map of reality to p-adicity.

It is interesting question what this might mean from the point of view

of quantum computation. Selves are after all subsystems, whose subsystem

can perform quantum jumps (if TGD is correct). Is strong NMP would hold

and world would be purely real there would exist no self-hierarcy and self

hierarchy is absolutely crucial for conscious cognition.

Thus it would seem that p-adic physics is absolutely crucial for the

understanding of quantum computers.

Best,

MP

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