# QFT in Quantum Computing and Control Theory?

Is QFT being applied to quantum computing and control theory?

I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it were a course with prequisites of QFT, not a lot of people would have attended the course).

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"Quantum field theory" is more or less the universally spoken language of modern quantum physics at the research level, regardless of the energy scale. There appears to be widespread confusion that it is somehow a fundamentally different theory than "ordinary quantum mechanics", but this is not so. It is a compact notation that facilitates the treatment of many-particle systems and takes into account the exclusion principle.

The clearest explanation of the connection between the first and second quantization that I am aware of appears in the book Statistical Mechanics: A Set Of Lectures by Feynman. Among other things, it is proved that the first and second quantizations are fully equivalent, as the latter is developed directly from the former.

In short, the answer to your question is yes, but in a vacuous sense.

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While both theories are "quantum", is there not a clear difference between the two in that one integrates Special Relativity while the other does not? I'm not up to date in the latest quantum computing developments, but my guess would be that the true answer is rather that SR is not relevant for it. –  David M. R. Mar 21 '13 at 8:17
I'd naively interpret the quantum mechanics of quantum computing to be that section of the formalism which doesn't deal with explicit spatial dependence. Even if the framework (Hilbert spaces, yada yada) is the same, the papers on computing/optics look like "$|010\rangle$" while the papers on high energy physics look like "$\int \Psi(x)|\Omega\rangle$" –  NikolajK Mar 21 '13 at 8:17
@DavidM.R. QFT is used for both relativistic and nonrelativistic physics. E.g. see Many Particle Physics by Mahan (or the book by Feynman mentioned earlier). The thing that second quantization deals with fundamentally is coping with multiple particles and the exclusion principle in a way that is not excessively laborious. –  Joshua Barr Mar 21 '13 at 8:20
@JoshuaBarr: Thanks for the clear-up. –  David M. R. Mar 21 '13 at 8:29