refs

codes/classical/bits/easy/one_hot.yml

@@ -22,11 +22,15 @@ description: |
 realizations:
   - 'The bi-quinary code, a combination of one-hot 1-in-2 and 1-in-5 one-hot codes to encode decimal digits, was used in several early computers (\cite{doi:10.1201/9781315115870}, Ch. 27).'
   - 'Marking the state of a finite automaton \cite{doi:10.1109/43.41505}.'
+  - 'Encoding the output of the different classes of a classifier neural network \cite{manual:{Potdar, Kedar, Taher S. Pardawala, and Chinmay D. Pai. "A comparative study of categorical variable encoding techniques for neural network classifiers." International journal of computer applications 175.4 (2017): 7-9.}}. One-hot codes are the primary codes used in multiclass classification \cite{doi:10.1142/7238,arxiv:0711.2914,doi:10.5120/ijca2017915495,doi:10.1162/08997660151134334}.'
+
 
 relations:
   parents:
     - code_id: binary_cyclic
     - code_id: constant_weight
+    - code_id: ecoc
+      detail: 'One-hot codes are the primary codes used in multiclass classification \cite{doi:10.1142/7238,arxiv:0711.2914,doi:10.5120/ijca2017915495,doi:10.1162/08997660151134334}.'
   cousins:
     - code_id: ppm
       detail: 'The PPM code is an continuous analogue of the one-hot code.'

codes/classical/properties/block/ecoc.yml

@@ -11,6 +11,7 @@ introduced: '\cite{arxiv:cs/9501101,manual:{Allwein, Erin L., Robert E. Schapire
 description: |
   A length-\(n\) binary or ternary (over \(\{\pm 1,0\}\)) block code used to convey information about classes to classifiers in multiclass machine learning.
   Rows of the code's generator matrix denote different classes, while columns correspond to classifiers.
+  The \(\pm 1\) elements can be used to distinguish between a pair of chosen classes, while a zero entry correspond to a classifier ignoring that particular class.
 
   A \textit{data-driven ECOC (DECOC)} \cite{doi:10.1016/j.patcog.2007.05.020} is an ECOC whose design takes into account features of the data that is to be classified.
   Not always decoded using the Hamming metric.
@@ -39,10 +40,6 @@ relations:
       detail: 'Hadamard codes and subcodes can be used as ECOCs \cite{arxiv:cs/9501101,doi:10.1145/307400.307429,doi:10.1007/978-3-540-45080-1_51}.'
     - code_id: bch
       detail: 'BCH codes can be used as ECOCs \cite{arxiv:cs/9501101}.'
-    - code_id: one_hot
-      detail: 'One-hot codes are the primary codes used in multiclass classification \cite{doi:10.1142/7238,arxiv:0711.2914,doi:10.5120/ijca2017915495,doi:10.1162/08997660151134334}.'
-    - code_id: one_vs_one
-      detail: 'One-vs-one codes are often used in multiclass classification because they separate the muilticlass task into several two-class tasks  \cite{doi:10.1142/7238}.'
 
 
 # Begin Entry Meta Information

codes/classical/q-ary_digits/easy/one_vs_one.yml

@@ -14,22 +14,26 @@ alternative_names:
   - 'One-against-one (1A1) code'
 
 description: |
-  A length-\(n\) ternary code over \(\{\om 1,0\}\) whose whose generator matrix has columns with one \(+1\), one \(-1\), and with the rest of the entries zero.
+  A length-\(n\) ternary code over \(\{\pm 1,0\}\) whose whose generator matrix has columns with one \(+1\), one \(-1\), and with the rest of the entries zero.
 
   See \cite[Tab. 6.3]{doi:10.1142/7238} for an example, whose generator matrix is
   \begin{align}
+  \left[
   \begin{array}{cccccc}
   1 & 1 & 1 & 0 & 0 & 0 \\
   -1 & 0 & 0 & 1 & 1 & 0 \\
   0 & -1 & 0 & -1 & 0 & 1 \\
   0 & 0 & -1 & 0 & -1 & -1 \\
-  \end{array}~.
+  \end{array}
+  \right]~.
   \end{align}
 
 relations:
   parents:
     - code_id: q-ary_digits_into_q-ary_digits
     - code_id: constant_weight
+    - code_id: ecoc
+      detail: 'One-vs-one codes are often used in multiclass classification because they separate the muilticlass task into several two-class tasks  \cite{doi:10.1142/7238}.'
 
 
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codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml

@@ -12,6 +12,7 @@ introduced: '\cite{arxiv:quant-ph/0304153,arxiv:2005.10910,arxiv:2305.07023}'
 
 alternative_names:
   - '\(((7,2,3))\) icosahedral code'
+  - 'Kubischta-Teixeira code'
 
 
 description: |

codes/quantum/qubits/permutation_invariant/qubit_permutation_invariant.yml

@@ -26,6 +26,9 @@ description: |
 protection: |
   Permutation invariant qubit codes of distance \(d\) can protect against \(d-1\) deletion errors \cite{arxiv:2001.08405,arxiv:2004.00814}, i.e., erasures of subsystems at unknown locations.
 
+features:
+  general_gates:
+    - 'There is a measurement-free code-switching protocol between a qubit stabilizer code and a PI qubit code \cite{arxiv:2411.13142}.'
 
 features:
   decoders:
@@ -38,6 +41,9 @@ relations:
   parents:
     - code_id: qubits_into_qubits
     - code_id: permutation_invariant
+  cousins:
+    - code_id: qubit_stabilizer
+      detail: 'There is a measurement-free code-switching protocol between a qubit stabilizer code and a PI qubit code \cite{arxiv:2411.13142}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/qubits_into_qubits.yml

@@ -153,6 +153,7 @@ features:
       The measurement threshold is the maximum total probability that a single qubit is measured in a random \(X\), \(Y\), or \(Z\) basis at which the logical information is still recoverable.
       The measurement threshold is at least as large as the erasure threshold \cite[Thm. 4]{arxiv:2402.00145}.
       \end{defterm}'
+    - 'There is a dynamical phase transition between a bounded-error and an unbounded-error phase for a model of qubits weakly coupled to a refrigerator \cite{arxiv:2411.12805}.'
 
 notes:
   - 'There is a relation between one-way entanglement distillation protocols and QECCs \cite{arxiv:quant-ph/9604024}.'

codes/quantum/qubits/reinforcement_learning.yml

@@ -7,11 +7,11 @@ code_id: reinforcement_learning
 physical: qubits
 logical: qubits
 
-name: 'Neural network code'
+name: 'Neural network quantum code'
 introduced: '\cite{arxiv:1802.05267,arxiv:1806.08781,arxiv:1812.08451}'
 
 description: |
-  An approximate code obtained from a numerical optimization involving a reinforcement learning agent.
+  An approximate qubit code obtained from a numerical optimization involving a reinforcement learning agent.
 
 protection: |
   Depends on the parameter being optimized.

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -150,6 +150,7 @@ features:
     - 'Correlated decoding can improve performance of Clifford and non-Clifford entangling gates \cite{arxiv:2403.03272}.'
     - 'Detector graphs \cite{arxiv:2103.02202,arxiv:2303.15933} and detector error models \cite{arxiv:2407.13826} can be used to design syndrome extraction circuits and logical measurements.'
     - 'Fault-tolerant constant-depth unencoder transforming logical states into physical states using single-qubit measurements \cite{arxiv:2408.06299}.'
+    - 'Degenerate erasure decoder showing near ML decoding for various codes \cite{arxiv:2411.13509}.'
 
   fault_tolerance:
     - 'Gates in the \term{Clifford hierarchy} can be done using \textit{gate teleportation}, in which a gate can be obtained from a particular \textit{magic state} \cite{arxiv:quant-ph/9908010,arxiv:quant-ph/0002039}.