When Only Topology Matters
arXiv:2102.03178
Abstract
Graphical languages are symmetric monoidal categories presented by generators and equations. The string diagrams notation allows to transform numerous axioms into low dimension topological rules we are comfortable with as three dimensional space citizens. This aspect is often referred to by the Only Topology Matters paradigm (OTM). However OTM remains quite informal and its exact meaning in terms of rewriting rules is ambiguous. In this paper we define three precise aspects of the OTM paradigm, namely flexsymmetry, flexcyclicity and flexibility of Frobenius algebras. We investigate how this new framework can simplify the presentation of known graphical languages based on Frobenius algebras.
arXiv commentThe paper contains some errors that have to be fixed
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- The Qudit ZH-Calculus: Generalised Toffoli+Hadamard and Universality
- Completeness of the ZH-calculus
- Building Qutrit Diagonal Gates from Phase Gadgets
- Complete ZX-calculi for the stabiliser fragment in odd prime dimensions