Normalizing Resistor Networks

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.