Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)

• URL: http://arxiv.org/abs/2404.07828v2
• Date: Mon, 12 Aug 2024 11:20:55 GMT
• Title: Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)
• Authors: Aleks Kissinger, John van de Wetering,
• Abstract summary: 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 involving ZX-diagrams, called spider nest identities, can be captured using the ZX-calculus, and all such identities can be proved inductively from a single new rule. This can be combined with the ZX picture of CSS codes, developed in the Clifford "grokking" paper, to give a simple characterisation of the set of rules at the third level of the Clifford hierarchy implementable in an arbitrary CSS
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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