refs

codes/classical/matrices/tensor.yml

@@ -62,10 +62,7 @@ relations:
       detail: 'Tensor-product codes are examples of parallel concatenation \cite{doi:10.1109/TIT.2005.846392}.'
     - code_id: concatenated
       detail: 'Tensor-product codes can be viewed as serial concatenated codes \cite{doi:10.1109/TIT.2005.846392}.'
-  cousins:
-    - code_id: galois_polynomial
-      detail: 'Product codes constructed from a self-orthogonal and an arbitrary RS code yields an RS code \cite{arxiv:quant-ph/0703181}.'
-
+
 
 # Begin Entry Meta Information
 _meta:

codes/quantum/qubits/stabilizer/qldpc/homological/check_product.yml

@@ -17,13 +17,14 @@ relations:
   parents:
     - code_id: qubit_generalized_homological_product_css
     - code_id: qltc
-      detail: 'Quantum check-product constructions yield an sLTC code with constant soundness \(2\rho\) from a classical LTC code with soundness \(\rho\).
-      While these are the first bona-fide QLTC code family because they admit asymptotically constant soundess, they are not practical because their distance is two.'
+      detail: 'Quantum check-product constructions yield an sLTC code with constant soundness \(2\rho\) from a classical LTC code with soundness \(\rho\) \cite{arxiv:2209.11405}. While these are the first bona-fide QLTC code family because they admit asymptotically constant soundness, they are not practical because their distance is two.'
   cousins:
     - code_id: tensor
       detail: 'Quantum check-product codes extend the concept of a check product, which yields the dual of a tensor code, to a product between a classical and a quantum code.'
+    - code_id: quantum_tensor_product
+      detail: 'Quantum check-product codes extend the concept of a check product, which yields the dual of a tensor code, to a product between a classical and a quantum code.'
     - code_id: distance_balanced
-      detail: 'Quantum check-product code constructions use distance balancing to increase distance.'
+      detail: 'Quantum check-product code constructions use distance balancing to increase distance \cite{arxiv:2209.11405}.'
 
 # Begin Entry Meta Information
 _meta:

codes/quantum/qubits/stabilizer/quantum_tensor_product.yml

@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: quantum_tensor_product
+physical: qubits
+logical: qubits
+
+name: 'Quantum tensor-product code'
+introduced: '\cite{arxiv:quant-ph/0703181,arxiv:1605.09598}'
+
+description: |
+  CSS code constructed from a tensor code. In some cases, only one of the classical codes forming the tensor code needs to be self-orthogonal. 
+
+relations:
+  parents:
+    - code_id: qubit_css
+  cousins:
+    - code_id: tensor
+    - code_id: reversible
+      detail: 'Reversible cyclic codes can be used to construct quantum tensor-product codes \cite{arxiv:1605.09598}.'
+    - code_id: q-ary_cyclic
+      detail: 'Reversible cyclic codes can be used to construct quantum tensor-product codes \cite{arxiv:1605.09598}.'
+    - code_id: mds
+      detail: 'MDS codes can be used to construct quantum tensor-product codes \cite{arxiv:1605.09598}.'
+    - code_id: galois_polynomial
+      detail: 'Product codes constructed from a self-orthogonal and an arbitrary RS code yields an RS code \cite{arxiv:quant-ph/0703181}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-18'

codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml

@@ -46,6 +46,10 @@ relations:
     - code_id: reed_muller
     - code_id: quantum_convolutional
       detail: 'Quantum convolutional codes can be derived from quantum Reed-Muller codes \cite{arxiv:quant-ph/0701037}.'
+    - code_id: eastab
+      detail: 'EA versions of quantum RM codes and their quantum tensor-product variants can be constructed \cite{arxiv:2303.08294}.'
+    - code_id: quantum_tensor_product
+      detail: 'EA versions of quantum RM codes and their quantum tensor-product variants can be constructed \cite{arxiv:2303.08294}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/ea_stabilizer/ea_galois_stabilizer.yml

@@ -14,6 +14,9 @@ description: |
   A Galois-qudit stabilizer code constructed using a variation of the stabilizer formalism designed to utilize pre-shared entanglement between sender and receiver.
   A code is typically denoted as \([[n,k;e]]_q\) or \([[n,k,d;e]]_q\), where \(d\) is the distance of the underlying non-EA \([[n,k,d]]_q\) code, and \(e\) is the number of required pre-shared maximally entangled Galois-qudit maximally entangled states.
 
+features:
+  decoders:
+    - 'Syndrome extraction and computation based on classical additive codes \cite{doi:10.1103/PhysRevA.103.042420}.'
 
 relations:
   parents:
@@ -22,7 +25,7 @@ relations:
     - code_id: galois_stabilizer
       detail: 'Pure Galois-qudit codes can be used to make EA Galois-qudit stabilizer codes \cite{arxiv:1105.5872}\cite[Thm. 10]{arxiv:2010.07902}.'
     - code_id: galois_grs
-      detail: 'Galios-qudit GRS codes can be used to construct EA Galois-qudit stabilizer codes \cite{arxiv:1606.00134}.'
+      detail: 'Galios-qudit GRS codes can be used to construct EA Galois-qudit stabilizer codes \cite{arxiv:1606.00134,doi:10.1007/s11128-021-03028-w}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/ea_stabilizer/ea_mds.yml

@@ -20,7 +20,7 @@ relations:
   cousins:
     - code_id: quantum_mds
     - code_id: mds
-      detail: 'MDS codes give rise to families of EA Galois-qudit codes that saturate the original Singleton bound \cite{arxiv:1602.02235}.'
+      detail: 'MDS codes give rise to families of EA Galois-qudit codes that saturate the original (erroneous) EAQECC Singleton bound \cite{arxiv:1602.02235}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml

@@ -63,6 +63,8 @@ features:
     - 'Encoder with \(O(n^2)\) gates can be determined in classical runtime of order \(O(n^3)\) \cite{arxiv:quant-ph/0211014}.'
   general_gates:
     - '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}.'
+  decoders:
+    - 'Syndrome extraction and computation based on classical additive codes \cite{doi:10.1103/PhysRevA.103.042420}.'
 
 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}. 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}}.'