Normalizing Resistor Networks
- URL: http://arxiv.org/abs/2303.11839v3
- Date: Thu, 14 Dec 2023 12:57:21 GMT
- Title: Normalizing Resistor Networks
- Abstract summary: This paper describes a rewriting system for resistor circuits over any positive division rig.
We show how these transformations can be organized into a confluent and terminating rewriting system on the category of resistor circuits.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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