Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)
arXiv:2404.07828 · doi:10.4204/EPTCS.406.4
Abstract
This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX-calculus. In this paper we show that certain complex rules involving ZX-diagrams, called spider nest identities, can be captured succinctly using the scalable ZX-calculus, and all such identities can be proved inductively from a single new rule using the Clifford ZX-calculus. This can be combined with the ZX picture of CSS codes, developed in the first "grokking" paper, to give a simple characterisation of the set of all transversal diagonal gates at the third level of the Clifford hierarchy implementable in an arbitrary CSS code.
In Proceedings QPL 2024, arXiv:2408.05113
References in corpus (6)
- Magic state distillation with low overhead
- Diagonal gates in the Clifford hierarchy
- Classification of Small Triorthogonal Codes
- Transversal Diagonal Logical Operators for Stabiliser Codes
- Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)
- Quantum Circuit Optimization with AlphaTensor