Physics, Topology, Logic and Computation: A Rosetta Stone

Details Physics, Topology, Logic and Computation: A Rosetta Stone Physics, Topology, Logic and Computation: A Rosetta Stone

2009-03-02

arxiv.org/abs/0903.0340v3

Physics, topology, logic and compIn New Structures for Physics, ed. Bob Coecke, Lecture Notes in Physics vol. 813, Springer, B

Physics

Quantum Physics

73 pages, 8 encapsulated postscript figures

Scientific paper

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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