WebEastin-Knill) Theorem 1. Quantum error-correcting codes. Consider a QECC, where states and operations on a logical system Lare encoded into a physical system A, … WebDec 8, 2024 · The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely.

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WebMar 2, 2024 · The Eastin-Knill Theorem shows that the transversal gates always form a group and that moreover this group is a finite subgroup of the group of all unitaries. For … 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). $\endgroup$ how many wives did julius have

Equivalent $[\\![n,k,d]\\!]$ codes and transversal gates

WebComplex instruction set computing architecture for performing accurate quantum Z rotations with less magic Andrew J. Landahl1,2,3, and Chris Cesare2,3, y 1Advanced Device Technologies, Sandia National Laboratories, Albuquerque, NM, 87185, USA 2Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM, 87131, … 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? how many wives did king david have kjv