vix.ing · top · new · best · stats

Physics, Topology, Logic and Computation: A Rosetta Stone

2009/03/02 by John C. Baez, Mike Stay · 15 voices · 258 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computability, Logic, AI Algorithms #Computation #Computer science #Electrical engineering #Particle physics #Physics #Quantum Mechanics and Applications #Theoretical physics #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.CT #quant-ph

paper · pdf · doi:10.1007/978-3-642-12821-9_2

published in Lecture notes in physics, 95-172 (Springer Science+Business Media) · 73 pages, 8 encapsulated postscript figures

arxiv created 2009/06/06 · openalex publication_date 2010/01/01 · arxiv updated 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

Cited by

Discussions

Related