ref

codes/classical/properties/block/universally_optimal/t-designs.yml

@@ -36,7 +36,7 @@ description: |
   Designs also exist on groups.
   Designs on the unitary (projective unitary) group are called strong unitary (unitary) designs \cite{arXiv:quant-ph/0611002}, while \(t\)-designs on the permutation group are called permutation \(t\)-designs \cite{doi:10.1017/S0963548300001917} (a.k.a. \(t\)-wise independent permutations).
 
-  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, and Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}.
+  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}, and designs on vertex operator algebras (a.k.a. conformal designs) \cite{arxiv:arXiv:math/0701626}.
   Existence has been proven for combinatorial designs \cite{doi:10.1016/0012-365X(87)90061-6}, subspace designs \cite{doi:10.1016/j.jcta.2014.06.001,arxiv:2212.00870}, as well as designs on continuous topological spaces \cite{doi:10.1016/0001-8708(84)90022-7,arxiv:1111.5900,arxiv:1112.4900}.
 
 #  when restricted to act on distinct \(t\)-tuples; see \cite[Remarks 6-7]{arXiv:2404.14648}

codes/quantum/qudits/small/qudit_5_1_3.yml

@@ -14,7 +14,12 @@ introduced: '\cite{arxiv:quant-ph/9702033,arxiv:quant-ph/9703048}'
 
 description: |
   Modular-qudit stabilizer code that generalizes the five-qubit perfect code using properties of the multiplicative group \(\mathbb{Z}_q\) \cite{arxiv:quant-ph/9702033}; see also \cite[Thm. 13]{arxiv:quant-ph/9703048}. It has four stabilizer generators consisting of \(X Z Z^\dagger X^\dagger I\) and its cyclic permutations.
-  A concise expression for a set of codewords can be found in \cite[Sec. VI.B]{arxiv:1902.07714}.
+
+  The components of the encoding isometry in the computational basis (with \(a\) being the logical qubit index) are \cite[Sec. VI.B]{arxiv:1902.07714}
+  \begin{align}
+      T_{aklmnp}=\d_{a,k+l+m+n+p}^{\Z_{q}}\frac{1}{q^{2}}\omega^{km+kn+ln+lp+mp}~,
+  \end{align}
+  where \(\omega\) is a primitive \(q\)th root of unity, and where \(\delta^{\Z_{q}}\) is the \hyperref[topic:group-pauli]{\(\mathbb{Z}_q\) Kronecker-delta function}.
 
 protection: 'Protects against a single error on any one qudit. Detects two-qudit errors.'
 

users/users_db.yml

@@ -34,10 +34,6 @@
 
 
 #
-- user_id: MatthewSteinberg
-  name: 'Matthew Steinberg'
-  gscholaruser: lGZwMRAAAAAJ
-
 - user_id: GregKuperberg
   name: 'Greg Kuperberg'
   gscholaruser: OrKdXCgAAAAJ