Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929629339582464 |
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| author | Kissinger, Aleks van de Wetering, John |
| author_facet | Kissinger, Aleks van de Wetering, John |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates) Kissinger, Aleks van de Wetering, John Quantum Physics 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. |
| title | Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates) |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.07828 |