WebDec 15, 2024 · The Eastin-Knill theorem may be viewed as a restric-tion on codes covariant with respect to some continuous symmetry group Gthat acts as a … 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 …
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WebBTW, it seems that a simple yet rigorous non-equivalence proof might be constructed for two color codes or two CSS codes deriving from self-dual doubly even classical codes (since in those cases the transversal group coincides with the Cliffords and we can appeal to Eastin-Knill theorem to rule out other transversal gates). $\endgroup$ WebApr 15, 2024 · More specifically, it is known by the Eastin-Knill theorem [11] that if a (finite-dimensional) code implements any continuous group of logical gates transversally (such … how to remove mold from clothes
Eastin-Knill Theorem and its Implications - University of …
http://www.cs.tulane.edu/quantum/slides/PR18/MURIFinal.pptx The Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can transversely implement a universal gate set. Since quantum computers are … See more The approximate version of the Eastin–Knill theorem states: "If a code admits a continuous symmetry pertaining to a Lie group and corrects erasure with fixed accuracy, then for each logical qubit, a number of physical … See more The Eastin–Knill theorem does not prohibit protocols that provide fault tolerant quantum computation. Some methods of getting around … See more WebOct 18, 2024 · However, the Eastin-Knill theorem says that not all unitaries in a universal set can be implemented transversally. So there will be (at least) one gate in the set with a much higher depth, and that may be your critical case. In many implementations, the non-transversal gate is chosen to be the T gate. ... noridian webinar part a