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[0903.0340] Physics, Topology, Logic and Computation: A Rosetta Stone
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Quantum Physics
Title: Physics, Topology, Logic and Computation: A Rosetta Stone
Authors: John C. Baez, Mike Stay
(Submitted on 2 Mar 2009 (v1), last revised 6 Jun 2009 (this version, v3))
Abstract: In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.
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| Comments: | 73 pages, 8 encapsulated postscript figures |
| Subjects: | Quantum Physics (quant-ph); Category Theory (math.CT) |
| Journal reference: | Physics, topology, logic and compIn New Structures for Physics, ed. Bob Coecke, Lecture Notes in Physics vol. 813, Springer, Berlin, 2011, pp. 95-174 |
| Cite as: | arXiv:0903.0340 [quant-ph] |
| | (or arXiv:0903.0340v3 [quant-ph] for this version) |
Submission history
From: John Baez [view email]
[v1] Mon, 2 Mar 2009 20:38:42 GMT (136kb)
[v2] Tue, 3 Mar 2009 03:09:13 GMT (136kb)
[v3] Sat, 6 Jun 2009 00:45:58 GMT (136kb)
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