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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorIan_Durham
   • CommentTimeSep 6th 2010
   • (edited Sep 6th 2010)
   • PermaLink
   Author: Ian_Durham
   Format: MarkdownItexJust wondering if anyone here knows of a reference to anyone having used categories in electrical circuit analysis. I'm trying to better understand the analogies between quantum circuits and classical (electrical) circuits and it seems like category theory might be quite useful for this. Edit: Let me add that one of the reasons I'm interested in understanding this is because I am working on systems that are "hybrids," i.e. they use standard classical components (e.g. logic gates) as well as quantum components (e.g. quantum logic gates). Experimentally, making such a thing is relatively straightforward (any physical implementation of a quantum logic gate necessarily has some classical electronic components to it), but there doesn't seem to be a strong theoretical bridge allowing for further design.

   Just wondering if anyone here knows of a reference to anyone having used categories in electrical circuit analysis. I’m trying to better understand the analogies between quantum circuits and classical (electrical) circuits and it seems like category theory might be quite useful for this.

   Edit: Let me add that one of the reasons I’m interested in understanding this is because I am working on systems that are “hybrids,” i.e. they use standard classical components (e.g. logic gates) as well as quantum components (e.g. quantum logic gates). Experimentally, making such a thing is relatively straightforward (any physical implementation of a quantum logic gate necessarily has some classical electronic components to it), but there doesn’t seem to be a strong theoretical bridge allowing for further design.

2. • CommentRowNumber2.
   • CommentAuthorEric
   • CommentTimeSep 7th 2010
   • PermaLink
   Author: Eric
   Format: MarkdownItexJohn talked about this a bit in his TWF's not too long ago and likely gave some references. Don't have a direct link, but it shouldn't be too hard to find.

   John talked about this a bit in his TWF’s not too long ago and likely gave some references. Don’t have a direct link, but it shouldn’t be too hard to find.

3. • CommentRowNumber3.
   • CommentAuthorIan_Durham
   • CommentTimeSep 8th 2010
   • PermaLink
   Author: Ian_Durham
   Format: MarkdownItexOK, cool, thanks.

   OK, cool, thanks.