Quantum Bayesian Networks

November 9, 2014

Are Feynman Path Integrals Useful In Quantum Computing?

Filed under: Uncategorized — rrtucci @ 5:20 am

Contemporary High Energy physicists seldom formulate their new theories in the Schroedinger picture (or associated operator pictures like the Heisenberg or Interaction pictures). They prefer instead to formulate their theories in terms of Feynman path integrals because such integrals exhibit the symmetries of the theory more explicitly without having to worry about operator ordering. So an important question to ask is, are Feynman path integrals useful in Quantum Computing too? I would say, yes, absolutely. This is how I personally see it:

operator pictures ~ quantum circuits

Feynman path integral picture ~  quantum Bayesian networks

The analogy is not perfect, but it’s very close, in my opinion.

A related post is:
Quantum Circuits in the Dirac, Quayle and Bayes Conventions

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4 Comments »

  1. I found this to be a deeper picture.

    http://en.wikipedia.org/wiki/Phase_space_formulation

    Comment by Elangel Exterminador — November 9, 2014 @ 9:10 am

  2. Thanks very much for the reference, Angel. I’ll have to think much more about this. At first blush, I would say:

    I think your wikipedia article gives a differential formulation (in terms of operators), rather than an integral formulation (in terms of sums over histories, which is what Feynman path integrals are all about). I guess my contention is that quantum Bayesian networks are more appropriate for an integral formulation and quantum circuits are more appropriate for a differential formulation. One can also make a distinction between Hamiltonian and Lagrangian formulations, but I think both of those can be put in either differential or integral forms.

    Comment by rrtucci — November 9, 2014 @ 3:57 pm


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