Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions

Understand

Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms.

• We improve on this method by studying stabiliser decompositions of ZX diagrams involving the triangle operation.
• We show that this technique greatly speeds up the simulation of quantum circuits involving multi-controlled gates which can be naturally represented using triangles.
• We implement our approach in the QuiZX library and demonstrate a significant simulation speed-up (up to multiple orders of magnitude) for random circuits and a variation of previously used benchmarking circuits.