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What I mean by effective in the question refers to the time and space requirements for sending information over a quantum communications channel. Having read "Mike and Ike" but doing no independent research on the question, my initial impression is that a channel using an effect from quantum field theory e.g. quantum electrodynamics would be more powerful over a narrower range of algorithms than an "ordinary" or "vanilla" quantum computer i.e. one that derived information from its steady-state behavior e.g. quantum electrostatics.

Are there any quantum information theorists working on proving whether this is true or false?

EDIT:

Allow me to quote from the portion of the book the provoked the question (p.6):

At the time of writing it is not clear whether Deutsch’s notion of a Universal Quantum Computer is sufficient to efficiently simulate an arbitrary physical system. Proving or refuting this conjecture is one of the great open problems of the field of quantum computation and quantum information. It is possible, for example, that some effect of quantum field theory or an even more esoteric effect based in string theory, quantum gravity or some other physical theory may take us beyond Deutsch’s Universal Quantum Computer, giving us a still more powerful model for computation. At this stage, we simply don’t know.

I simply assume that a more powerful model of computation would give rise to a more efficient communications channel. Unless there has been a proof of the universality of a Universal Quantum Computer it seems that whoever said 'quantum is quantum' is very much getting ahead of themselves.

Now, with all that being said, I reiterate my previous question: are there any quantum information theorists working on proving whether this is true or false?

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Your comparison between quantum field theory and quantum elecrotstatics seems a nonsense. Quantum is quantum. Your question should be reformulated as "Quantum channels vs Classical channels". Maybe this recent reference could be useful to you, see for instance chapter 12, page 305 –  Trimok Jun 3 '13 at 10:07
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Are you speaking about quantum channel or quantum computers ? I have the feeling you mix the two, and I don't know how you manage to make any sens from Nielsen and Chuang's book while keeping this confusion. –  Frédéric Grosshans Jun 3 '13 at 11:34
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With your edit, the question is now clear. You are speaking about computing, not about communication channels. –  Frédéric Grosshans Jun 4 '13 at 9:54

3 Answers 3

up vote 1 down vote accepted

Would Quantum Field Theory allow more powerful computation than the standard quantum computing model ?

The question above is how I understood your question after your edit. It is the question I try to answer below.

As far as I know, the question is still formally open since it was asked in Nielsen and Chuang's book. However, in the 13 years (2000-2013) since the publication of this books, progress have been made. This 2000 paper deal with the simulation of topological field theories and this one from 2011 deals with scalar field theories. Both paper provide efficient simulation algorithm (to run on a quantum computer) of some quantum field theories, thereby showing that these theories do not allow to create a computer more powerful than the standard quantum computer.

If you want an accessible account on this question, you can read this answer by @Scott Aaronson, on cstheory.sx and this post on his blog.

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Thank you @FrédéricGrosshans for your patient and insightful answer. Apologies to the other people reading/commenting/answering, as my original formulation was not at all clear. –  user756 Jun 8 '13 at 15:32

Every single fiber optics cable in the world is a quantum channel. So a large percentage of information is currently being transmitted over quantum channels.

To explain further, the equations describing how the light propagates down the fiber optic cable are quantum. Theoretically, quantum information can be transmitted over fiber optic channels. Quantum cryptography can be used to distribute secret keys across a fiber optic cable, something which cannot be done with classical channels.

We currently treat fiber optic cables as classical devices for the purposes of communication. One can ask how much using the quantum effects would raise the amount of information that we could send using a given energy, and in the range of parameters which they are currently being used, the answer is "not much". And experimentally, we don't have anywhere close to the input devices and output devices that we would need to send real quantum information over fiber optical cables. If we could, we might be able to use this to build better telescopes.

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I'm not sure what is meant by 'quantum electrostatics' or what a 'vanilla' quantum computer is. Cutting edge quantum computers are not very capable or efficient today compared to classical (semiconductor) computers.

That said, quantum computing does offer communications and encryption (as well as computation and cryptography) mechanisms that can not be replicated using just classical channels, at least in theory. In practice, thus far, quantum computers are not a practical choice.

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There is currently no working quantum computer (and Dwave's machine is not a quantum computer), so I don't know what you mean by "cutting edge quantum computers". If on manage to construct some some one day, then @Peter Shor has shown that they can be vastly more efficient than classical computers for some problems (unless there a revolutionary classical algorithm for factorization is found). –  Frédéric Grosshans Jun 3 '13 at 11:32
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My definition of a quantum computer is more generous than yours: my view is that the demonstration of a single quantum gate is indeed a quantum computer, albeit not a very practical one, and in fact still experimental in nature. –  Joe Jun 3 '13 at 14:50

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