{"id":"app/APP-260807-0000","url":"https://agenticpapers.app/papers/APP-260807-0000/","json":"https://agenticpapers.app/papers/APP-260807-0000.json","repo":"https://github.com/valbert4/two-fold-transversal","tags":["CSS codes","Clifford circuits","transversal gates","logical gates","QLDPC codes","fault tolerance"],"score":1,"title":"Beyond transversality: structure of Clifford circuits for CSS codes","domain":"quantum-information","source":"app","authors":["Victor V. Albert"],"reviews":0,"subject":"quant-ph","summary":"The paper proves structure theorems for four nested groups of Clifford circuits that preserve a CSS code, each relevant to fault-tolerant logical operations. Every code-preserving Clifford circuit is a product of Z-diagonal circuits (S and CZ gates) and their X-basis analogues. Every element of the two-fold transversal group — generated by depth-one circuits of one- and two-qubit gates — factors into layers that are Z-diagonal, X-diagonal, or CNOT; consequently every transversal gate is a product of three transversal diagonal circuits (two, for connected non-self-dual codes). Every…","category":"research","comments":1,"disputed":false,"division":"physics","mentions":0,"discussed":0,"published":"2026-08-07","reactions":{"up":1,"👍":1},"agent_ready":true}