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caveat: the sort of exotic matter engineering in here is currently beyond the reach of our technology, but, that having been said:

Has their been any research on building models of these sorts of circuits?

Are there computations that would be more effective in circuits built from color superconductors than would be in ones built from electric superconductors?

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Color forces are not like electromagnetic ones. There exist no unbound color carrying particles analogous to the electron, because the forces increase with the distance rather than decrease and collective effects appear only within nuclei through residuals of the colored forces which attract the nucleons and hold them in the nuclei.

Collective effects are predicted by quantum chromodynamics to appear at very high temperatures in the quark-gluon plasma phase of matter. Plasma means

a phase of quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. This phase consists of asymptotically free quarks and gluons,a This happens at very high temperatures

The signatures of this are sought in the specifically designed ion collisions of the LHC experiments currently.

To answer your question: No, there are no materials that could be utilized to channel this plasma and create a "circuit" i.e. a color current, let alone a superconducting current, meaning a current that displays macroscopic quantum mechanical order and flows coherently.

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Note that the distance scales associated with "binding" for the purposes of "There exist no unbound ..." are those of the nucleon. Roughly one $\text{fm} = 10^{-15}\text{ m}$. –  dmckee Jan 11 '12 at 13:47
@anna v: You are right on Earth, but color superconductor is in a neutron star, so presumably, the OP wants to build circuitry on the surface of a neutron star, using nuclear material which is extensive thermodynamically. –  Ron Maimon Jan 11 '12 at 23:36
@RonMaimon That would be completely science fiction, since how could a human exist in a plasma environment or a quark gluon whatever? at least as far as we know? I am replying within physical bounds I guess. –  anna v Jan 12 '12 at 5:13
@anna v: Well,there is a the neutron star ordinary-matter crust, which is sort of like an atmosphere relative to the dense nuclear matter below. You could imagine building material stuff in the crust that then etches patterns into the nuclear material below, and propagates this to the color superconductor at the core (if it is accessible), etc, etc. It is science fiction, but that's what I thought OP was asking. I have no problem with your answer, which is in the realm of what's realizable in the next thousand years or so. –  Ron Maimon Jan 12 '12 at 5:24
What about color flavor locking? en.wikipedia.org/wiki/Color%E2%80%93flavor_locking –  deoxygerbe Jun 28 '13 at 2:09
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