~

codes/classical/bits/cyclic/binary_quad_residue.yml

@@ -35,6 +35,9 @@ relations:
       detail: 'Extended binary quadratic residue codes of length \(8m\) are self-dual doubly even codes \cite[pg. 82]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: lexicographic
       detail: 'The \([18,9,6]\) binary QR code is a lexicode \cite{doi:10.1109/TIT.1986.1057187}.'
+    - code_id: quasi_cyclic
+      detail: 'Binary QR codes are equivalent to double circulant codes for all \(n<200\) except 89 and 167 \cite{manual:{Beenker, G. J. M. "On double circulant codes." (1980).}}.'
+
 
 
 # Begin Entry Meta Information

codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml

@@ -7,8 +7,8 @@ code_id: q-ary_quad_residue
 physical: q-ary_digits
 logical: q-ary_digits
 
-name: '\(q\)-ary quadratic-residue (QR) code'
-short_name: '\(q\)-ary QR'
+name: 'Quadratic-residue (QR) code'
+short_name: 'QR'
 #introduced: ''
 
 description: |

codes/quantum/qubits/qubits_into_qubits.yml

@@ -133,6 +133,7 @@ features:
         C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~,
       \end{align}
       where \(P\) is any Pauli matrix, where \(C_1\) is the \hyperref[topic:pauli]{Pauli group}, and where \(C_2\) is the \hyperref[topic:clifford]{Clifford group}.
+      Gates for one qubit have been classified \cite{arxiv:2501.07939}.
       \end{defterm}'
     - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.'
     - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.'

codes/quantum/qudits/qudits_into_qudits.yml

@@ -56,6 +56,7 @@ features:
         C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~,
       \end{align}
       where \(P\) is any modular-qudit Pauli matrix, and \(C_1\) is the \hyperref[topic:qudit-pauli]{modular-qudit Pauli group}.
+      Gates for one prime-dimensional qudit have been classified \cite{arxiv:2501.07939}.
       \end{defterm}'
   decoders:
     - 'For few-qudit codes (\(n\) is small), decoding can be based on a lookup table. For infinite code families, the size of such a table scales exponentially with \(n\), so approximate decoding algorithms scaling polynomially with \(n\) have to be used. The decoder determining the most likely error given a noise channel is called the \textit{maximum-likelihood} (ML) decoder.'
@@ -65,6 +66,7 @@ features:
 
 notes:
   - 'Weight distribution of a code depends on the average entanglement of codewords \cite{arxiv:quant-ph/0310137,arxiv:2209.07607}.'
+  - 'Qudit Cirq library \cite{arxiv:2501.07812}.'
 
 
 relations: