[2306.02114] Light-Matter Interaction in the ZXW Calculus
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Quantum Physics

arXiv:2306.02114 (quant-ph)
[Submitted on 3 Jun 2023 (v1), last revised 31 Aug 2023 (this version, v2)]

Title:Light-Matter Interaction in the ZXW Calculus

Authors:Giovanni de Felice, Razin A. Shaikh, Boldizsár Poór, Lia Yeh, Quanlong Wang, Bob Coecke
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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.
Comments: In Proceedings QPL 2023, arXiv:2308.15489. 27 pages, lots of figures
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:2306.02114 [quant-ph]
  (or arXiv:2306.02114v2 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2306.02114
Journal reference: EPTCS 384, 2023, pp. 20-46
Related DOI: https://doi.org/10.4204/EPTCS.384.2

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Sat, 3 Jun 2023 13:55:34 UTC (161 KB)
[v2] Thu, 31 Aug 2023 06:55:48 UTC (72 KB)
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