Related papers: Light-Matter Interaction in the ZXW Calculus

Light-Matter Interaction in the ZXW Calculus

URL: http://arxiv.org/abs/2306.02114v2
Date: Thu, 31 Aug 2023 06:55:48 GMT
Title: Light-Matter Interaction in the ZXW Calculus
Authors: Giovanni de Felice, Razin A. Shaikh, Boldizs\'ar Po\'or, Lia Yeh, Quanlong Wang, Bob Coecke
Abstract summary: We introduce the infinite ZW calculus, a graphical language for linear operators on the bosonic Fock space. It is used to rewrite photonic circuits involving light-matter interactions and non-linear optical effects.
Score: 0.08388591755871733
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this paper, we develop a graphical calculus to rewrite photonic circuits involving light-matter interactions and non-linear optical effects. We introduce the infinite ZW calculus, a graphical language for linear operators on the bosonic Fock space which captures both linear and non-linear photonic circuits. This calculus is obtained by combining the QPath calculus, a diagrammatic language for linear optics, and the recently developed qudit ZXW calculus, a complete axiomatisation of linear maps between qudits. It comes with a 'lifting' theorem allowing to prove equalities between infinite operators by rewriting in the ZXW calculus. We give a method for representing bosonic and fermionic Hamiltonians in the infinite ZW calculus. This allows us to derive their exponentials by diagrammatic reasoning. Examples include phase shifts and beam splitters, as well as non-linear Kerr media and Jaynes-Cummings light-matter interaction.

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