Dear Andre and others,
But presently, I am not convinced that quantum computing can contribute significantly to category theory.
What the quantum information `hype' has done is injected some new blood in foundations of quantum mechanics research, an area which for several reasons had been suffocated by by the end of the previous century, despite the universal discomfort of the physics community with quantum mechanics. (a typical slogan which reflects this is: ``don't ask questions just compute'') One would expect that this surge of quantum foundations, which meanwhile has led to many novel ideas, approaches, and radically different manners to think about physics in general, will ultimately lead to new mathematics. Moreover, the natural guise of many of these new ideas is within category theory, a message that some including myself have been trying to pass on within the foundations of physics communitee, with moderate success. It moreover seems to me that identifying the appropriate mathematical structure to model a natural phenomenon is arguably as important as identifying the structure itself as a mathematical entity (cf Riemannian geometry and its re-discovery by Einstein et al to model relativistic space-time), even if it doesn't contribute to the area of mathematics in return. To my knowledge history has shown that ultimately it will do something in return, be it only due to the increased activity in the area, and it is here that money kicks in significantly. More boldly put, history seems to agree with the fact that in many cases important progress in fundamental physics fuels important progress in mathematics and vice versa. If category theory is, as has been claimed on this list, the greatest mathematical achievement of the 20th century, then one would expect it to have led to many important developments outside mathematics too, which may or may not inject something in to category theory in return. By only having `computer science' as a non-pure mathematics area in a list of now 15 subjects this seems not to be the case (yet). [I conceive quantum field theory in category-theoretic guise as a branch of mathematical physics of the pure mathematics kind] Doesn't this seriously undermine category theory's claim to fame? In this context there is the highly unfortunate fact that there are certain quite prominent people in the category theory community who think that any deviation from treating category as a branch of pure mathematics and pure mathematics only is a bad thing! Best wishes, Bob. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] Status: RO