From: scerir (scerir@libero.it)
Date: Wed Aug 06 2003 - 15:33:26 MDT
> Damn, damn and double damn.
> R.
Nielsen and Chuang have shown (1997) it is not possible to build a
general purpose quantum computer which can be programmed to perform
an arbitrary quantum computation. Thus a universal programmable quantum
gate array - a gate array which can be programmed to perform an
arbitrary unitary operation - that is to say a gate which could be
used to store and execute any program upon a quantum register - exists
only if one allows the gate array to operate in a 'probabilistic'
mode. Damn.
But it is possible to store, efficiently enough, an arbitrary unitary
operation in the pure state of a 'finite' quantum register, in a way
that it can be performed at a later time. Yep.
It follows, from the above, that no 'finite' dimensional programmable
gate array can be used to teleport an arbitrary unitary operation,
with a 100% efficiency. Damn. But it is possible to store, efficiently
enough, an arbitrary unitary operation in a quantum state which can
be teleported, later.
In example a N qu-bits program can be teleported from Alice to
Bob - consuming N e-bits of entanglement and N c-bits (classical
comunication from Alice to Bob)- so that Bob, even ignoring the
program, can perform it.
The teleportation protocol scheme can be also applied when portions
of a global quantum computation are performed at (very) distant
locations. Imagine Alice and Bob, in two distant locations, each of
them performing a portion of a quantum computation. Let us suppose
that the output qu-bits of Alice's QC are the input for Bob's QC,
or viceversa, etc. etc. Yep.
In these cases (above) the distributed quantum computing system is
based on the standard teleportation protocol scheme. Which means that
Alice must send (at least) a couple of c-bits to Bob telling him
the result of her 'Bell state' measurement and what to do.
But, we know, the classical communication channel is slow, especially
when Alice and Bob live in separated regions of ... a galaxy! Damn.
Now, what if Alice changes the standard teleportation protocol? That
is to say, what if Alice does not communicate anything to Bob? It
follows that Bob cannot be sure he got anything from Alice, and whether
or not he got the teleported 'right' quantum state (or the 'right'
qu-bits program). He just knows that the quantum state (or program)
he received from Alice is the 'right' one, within a certain probability,
25% in example. Damn.
Now is it possible to build a distributed quantum computing network
based (just) on the quantum communication channel which is fast but
also so risky? And what if Alice and Bob are the very same person?
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