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Mathematics > Category Theory

arXiv:2303.11839v3 (math)
[Submitted on 20 Mar 2023 (v1), last revised 14 Dec 2023 (this version, v3)]

Title:Normalizing Resistor Networks

Authors:Robin Cockett, Amolak Ratan Kalra, Priyaa Varshinee Srinivasan
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Abstract:Star to mesh transformations are well-known in electrical engineering, and are reminiscent of local complementation for graph states in qudit stabilizer quantum mechanics. This paper describes a rewriting system for resistor circuits over any positive division rig using general star to mesh transformations. We show how these transformations can be organized into a confluent and terminating rewriting system on the category of resistor circuits. Furthermore, based on the recently established connections between quantum and electrical circuits, this paper pushes forward the quest for approachable normal forms for stabilizer quantum circuits.
Comments: In Proceedings ACT 2023, arXiv:2312.08138
Subjects: Category Theory (math.CT); Quantum Physics (quant-ph)
Cite as: arXiv:2303.11839 [math.CT]
  (or arXiv:2303.11839v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2303.11839
Journal reference: EPTCS 397, 2023, pp. 70-83
Related DOI: https://doi.org/10.4204/EPTCS.397.5

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 20 Mar 2023 01:23:18 UTC (27,626 KB)
[v2] Mon, 5 Jun 2023 18:57:04 UTC (16,458 KB)
[v3] Thu, 14 Dec 2023 12:57:21 UTC (1,364 KB)
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