WebJun 3, 2024 · Indeed the entire family of $ [[2^{k+1}-1,1,3]] $ codes mentioned here Eastin Knill Theorem and groups of transversal gates is doubly even but not self dual. Shor's $ [[9,1,3]] $ code is a well known CSS code which is not self-dual and not doubly even. What is an example of a well known CSS code which is not doubly even but is self dual? WebNov 26, 2008 · Bryan Eastin, Emanuel Knill Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to …
Why do we care about the number of $T$ gates in a quantum …
WebThe first two conditions in the theorem are necessary. Condition 1 is a well known property of cardinality, while condition 2 follows from König's theorem . In Easton's model the … WebJul 17, 2024 · Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate codes which are covariant with respect to the … importance of family photos in child care
error correction - Why does code switching not allow for universal ...
WebMay 9, 2024 · Abstract Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. WebOct 27, 2024 · Eastin Knill Theorem and groups of transversal gates. Related. 5. In the Clifford group, is the center of $ \overline{\text{Cl}_n} \equiv\text{Cl}_n/U(1)$ trivial? 3. Eastin Knill Theorem and groups of transversal gates. 7. Prove that adding any non Clifford gate to the Clifford group yields a universal gate set. 7. WebIn an in depth follow up project, we generalized our theorem to approximate quantum error correcting codes, thereby proving a robust version of the Eastin-Knill theorem, and a … literal does not match format string n