Merge branch 'main' of https://github.com/errorcorrectionzoo/eczoo_data

codes/quantum/properties/block/block_quantum.yml

@@ -9,6 +9,7 @@ name: 'Block quantum code'
 
 description: |
   A code constructed in a multi-partite quantum system, i.e., a physical space consisting of a tensor product of \(n > 1\) identical subsystems, e.g., qubits, modular qudits, Galois qudits, or oscillators.
+  For finite dimensional codes, the dimension of the underlying subsystem is denoted by \(q\).
 
 protection: |
   Block codes protect from errors acting on a few of the \(n\) subsystems. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) subsystems, and corrects erasure errors on up to \(d-1\) subsystems.
@@ -29,6 +30,10 @@ features:
       A universal gate set for a finite-dimensional block quantum code cannot be transversal for any code that detects single-block errors due to the Eastin-Knill theorem \cite{arxiv:0811.4262}.
       \end{defterm}'
 
+notes:
+  - 'Tables of linear-programming upper bounds on general block quantum codes for various \(n\), \(k\), and \(q\), based on algorithms developed in Refs. \cite{doi:10.1007/978-3-540-37634-7_13,arxiv:2405.15057}, are maintained by M. Grassl at this \href{http://codetables.markus-grassl.de/}{website}.'
+
+
 relations:
   parents:
     - code_id: qecc

codes/quantum/qudits/stabilizer/qudit_stabilizer.yml

@@ -54,6 +54,7 @@ features:
     - 'Trellis decoder for prime-dimensional qudits, which builds a compact representation of the algebraic structure of the normalizer \(\mathsf{N(S)}\) \cite{arxiv:2106.08251}.'
 
 notes:
+  - 'Distance upper bounds for Galois-qudit stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Refs. \cite{doi:10.1007/978-3-540-37634-7_13,arxiv:2405.15057} and maintained by M. Grassl at this \href{http://codetables.markus-grassl.de/}{website}, hold for general modular-qudit codes because they are based on linear programming.'
   - 'A standardized definition of the qudit stabilizer group is developed in \cite{arxiv:1101.1519}.'
   - 'The number of modular-qudit stabilizer codes was determined in Refs. \cite{arxiv:quant-ph/0602001,arxiv:2209.01449}.'
 #   - 'For codes that do encode an integer number of \(q\)-dimensional qudits, i.e., \(K=q^k\), \(k\le 2n\) for composite \(q\)  \cite{arxiv:1101.1519}.'

codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml

@@ -65,7 +65,7 @@ features:
     - 'As opposed to modular qudits for composite \(q\), Galois qudits inherit most of the properties of the prime-qudit Clifford group due to the correspondence between a \(q=p^m\) Galois qudit and \(m\) prime qudits of dimension \(p\) \cite{doi:10.1109/18.959288}.'
 
 notes:
-  - 'Tables of bounds and examples of Galois-qudit stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Refs. \cite{doi:10.1007/978-3-540-37634-7_13,arxiv:2405.15057}, are maintained by M. Grassl at this \href{http://codetables.markus-grassl.de/}{website}.'
+  - 'Tables of bounds and examples of Galois-qudit stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Refs. \cite{doi:10.1007/978-3-540-37634-7_13,arxiv:2405.15057}, are maintained by M. Grassl at this \href{http://codetables.markus-grassl.de/}{website}. A modular-qudit stabilizer code with composite dimension \(q\) contains a subcode that is isomorphic to a \(p\)-dimensional prime-qudit stabilizer code for every prime factor \(p\) of \(q\), and the distance of the full stabilizer code is upper bound by the distance of this subcode \cite{manual:{Markus Grassl, private communication, 2024}}.'
   - 'The number of Galois-qudit stabilizer codes was determined in Ref. \cite{arxiv:quant-ph/0602001}.'
   - 'See Quantum Codes qudit stabilizer database, maintained by N. Aydin, P. Liu, and B. Yoshino, at this \href{http://quantumcodes.info/}{website}.'
 
@@ -79,7 +79,7 @@ relations:
     - code_id: galois_cws
       detail: 'Galois-qudit CWS codes whose underlying classical code is a linear \(q\)-ary code are Galois-qudit stabilizer codes containing a cluster-state codeword.'
     - code_id: qudit_stabilizer
-      detail: 'Recalling that \(q=p^m\), Galois-qudit stabilizer codes can also be treated as prime-qudit stabilizer codes on \(mn\) qudits, giving \(k=nm-r\) \cite{doi:10.1109/18.959288}. The case \(m=1\) reduces to conventional prime-qudit stabilizer codes on \(n\) qudits.'
+      detail: 'Recalling that \(q=p^m\), Galois-qudit stabilizer codes can also be treated as prime-qudit stabilizer codes on \(mn\) qudits, giving \(k=nm-r\) \cite{doi:10.1109/18.959288}. The case \(m=1\) reduces to conventional prime-qudit stabilizer codes on \(n\) qudits. A modular-qudit stabilizer code with composite dimension \(q\) contains a subcode that is isomorphic to a \(p\)-dimensional prime-qudit stabilizer code for every prime factor \(p\) of \(q\), and the distance of the full stabilizer code is bounded by the distance of this subcode \cite{manual:{Markus Grassl, private communication, 2024}}.'
     - code_id: q-ary_additive
       detail: 'Galois-qudit stabilizer codes are the closest quantum analogues of additive codes over \(GF(q)\) because addition in the field corresponds to multiplication of stabilizers in the quantum case.'
     - code_id: dual_additive
@@ -98,6 +98,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: MarkusGrassl
+      date: '2024-07-11'
     - user_id: VictorVAlbert
       date: '2022-07-22'
     - user_id: VictorVAlbert