diff --git a/codes/quantum/properties/qecc_finite.yml b/codes/quantum/properties/qecc_finite.yml index 4f5005ce8..447bc2df7 100644 --- a/codes/quantum/properties/qecc_finite.yml +++ b/codes/quantum/properties/qecc_finite.yml @@ -33,12 +33,13 @@ protection: | \begin{align} \Pi E_i^\dagger E_j \Pi = c_{ij}\, \Pi\qquad\text{for all \(i,j\),} \end{align} - where the \textit{QEC matrix} elements \(c_{ij}\) are arbitrary complex numbers. + where the \textit{QEC matrix} elements \(c_{ij}\) are arbitrary complex numbers. \end{defterm} The Knill-Laflamme conditions can alternatively be expressed in terms of the \hyperref[topic:complementary-channel]{complementary channel}, or in an information-theoretic way via a data processing inequality \cite{arxiv:quant-ph/9604022,arxiv:quant-ph/9702031}\cite[Eq. (29)]{arxiv:quant-ph/9604034}. They motivate higher-rank numerical ranges, which are generalizations of the numerical range of an operator \cite{arxiv:quant-ph/0511101,arXiv:math/0511278}. They have been extended to sequences of multiple errors and rounds of correction \cite{arxiv:2405.17567}. + The non-correctable contributions to the conditions can be arranged in a signature vector \cite{arxiv:2410.07983}. \begin{defterm}{Degeneracy} \label{topic:degeneracy} diff --git a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml index defa703eb..089dc0ee8 100644 --- a/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml +++ b/codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml @@ -39,6 +39,9 @@ relations: detail: 'The \(((7,2,3))\) Pollatsek-Ruskai code admits a transversal representation of the twisted \(1\)-group \(2I\) \cite{arxiv:2402.01638}.' - code_id: j_gross detail: 'The \(((7,2,3))\) Pollatsek-Ruskai code can be interpreted as a spin-\(7/2\) Clifford code \cite{arxiv:2005.10910}.' + cousins: + - code_id: steane + detail: 'The Pollatsek-Ruskai code can be continuously deformed to the Steane code \cite{arxiv:2410.07983}.' # Begin Entry Meta Information