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

@article{Baez2009PhysicsTL, title={Physics, Topology, Logic and Computation: A Rosetta Stone}, author={John C. Baez and Michael Stay}, journal={Lecture Notes in Physics}, year={2009}, volume={813}, pages={95-172} }

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”: a manifold representing spacetime, going between two manifolds representing space. This led to a burst of work on topological quantum field theory and “quantum topology”. But this was just the beginning: similar diagrams can be used to…

## 229 Citations

Computation and the Periodic Table

- Physics2009 24th Annual IEEE Symposium on Logic In Computer Science
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This talk is based on work in progress with Paul-Andre Mellies and Mike Stay and an important clue comes from the way symmetric monoidal closed 2-categories describe rewrite rules in the lambda calculus and multiplicative intuitionistic linear logic.

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- 2015

This thesis begins by demonstrating the effectiveness of string diagrams for practical calculations in category theory, and introduces a parameterized, duality based frame- work for coalgebraic logic, and proves that the semantics of these logics satisfy certain "institution conditions" providing harmony between syntactic and semantic transformations.

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- Physics
- 2010

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual…

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- 2017

We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor $GNS : \mathbf{Phys} \longrightarrow \ast\mathbf{Mod}$, based on the…

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A realization of a dagger-compact category that can model finite-dimensional quantum systems and explicitly allows for the interaction of systems of arbitrary, possibly unequal, dimensions is presented.

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- PhysicsCiE
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It is argued that partial recursive functions that according to Church’s thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops and can be addressed in the same way as Feynman divergences.

Embracing the Laws of Physics: Three Reversible Models of Computation

- Computer ScienceAdv. Comput.
- 2022

Interacting Quantum Observables: Categorical Algebra and Diagrammatics

- MathematicsArXiv
- 2009

The ZX-calculus is introduced, an intuitive and universal graphical calculus for multi-qubit systems, which greatly simplifies derivations in the area of quantum computation and information and axiomatize phase shifts within this framework.

Quantum picturalism

- Physics
- 2010

Why did it take us 50 years since the birth of the quantum mechanical formalism to discover that unknown quantum states cannot be cloned? Yet, the proof of the ‘no-cloning theorem’ is easy, and its…

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- Physics, Mathematics
- 2015

Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use…

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