Normalizing Resistor Networks
Category Theory
2023-12-15 v3 Quantum Physics
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.
Cite
@article{arxiv.2303.11839,
title = {Normalizing Resistor Networks},
author = {Robin Cockett and Amolak Ratan Kalra and Priyaa Varshinee Srinivasan},
journal= {arXiv preprint arXiv:2303.11839},
year = {2023}
}
Comments
In Proceedings ACT 2023, arXiv:2312.08138