~

codes/classical/bits/easy/dual_hamming/repetition.yml

@@ -22,9 +22,10 @@ features:
 
   decoders:
     - 'Calculate the Hamming weight \(d_H\) of an error word. If \(d_H\leq \frac{n-1}{2}\), decode the code as 0. If \(d_H\geq \frac{n+1}{2}\), decode the code as 1.'
-    - 'Local automaton decoder for the repetition code on a 2D lattice based on Toom''s rule \cite{manual:{A. L. Toom, “Nonergodic Multidimensional System of Automata”, Probl. Peredachi Inf., 10:3 (1974), 70–79; Problems Inform. Transmission, 10:3 (1974), 239–246},manual:{Toom, Andrei L. "Stable and attractive trajectories in multicomponent systems." Multicomponent random systems 6 (1980): 549-575.},doi:10.1007/978-1-4612-2168-5_18}.'
+    - 'Local automaton decoder for the repetition code on a 2D lattice based on Toom''s rule \cite{manual:{A. L. Toom, “Nonergodic Multidimensional System of Automata”, Probl. Peredachi Inf., 10:3 (1974), 70–79; Problems Inform. Transmission, 10:3 (1974), 239–246},manual:{Toom, Andrei L. "Stable and attractive trajectories in multicomponent systems." Multicomponent random systems 6 (1980): 549-575.},doi:10.1007/978-1-4612-2168-5_18,doi:10.1147/rd.481.0005}.'
     - 'Local automaton decoder for the repetition code on a 1D lattice by Gacs that is translation-invariant, that does not require synchronization of local clocks, and that has a constant encoding rate \cite{doi:10.1145/800061.808730,arxiv:math/0003117}.'
     - 'Local automaton decoder for the repetition code on a 1D lattice by Tsirelson \cite{doi:10.1007/BFb0070081}.'
+    - 'Local automaton decoder obtained from reinforcement learning \cite{arxiv:2408.09524}.'
 
   threshold:
     - 'Suppose each bit has probability \(p\) of being received correctly, independent for each bit. The probability that a repetition code is received correctly is \(\sum_{k=0}^{(n-1)/2}\frac{n!}{k!(n-k)!}p^{n-k}(1-p)^{k}\). If \(\frac{1}{2}\leq p\), then one can always increase the probability of success by increasing the number of physical bits \(n\); see section 2.2.1 Ref. \cite{arxiv:2111.08894} for a pedagogical explanation.'

codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml

@@ -66,7 +66,7 @@ features:
       \end{defterm}'
 
   decoders:
-    - 'A \textit{local automaton decoder} applies local rules to each small region of sites in a lattice geometry. Such decoders do not require any potentially non-local classical post-processing of error syndromes.'
+    - 'A \textit{local automaton decoder} (a.k.a. measurement-free local error correction) applies local rules to each small region of sites in a lattice geometry. Such decoders do not require any potentially non-local classical post-processing of error syndromes.'
     - 'Clustering decoder \cite{doi:10.7907/AHMQ-EG82,arxiv:1112.3252}.'
     - 'Quantum neural-network (QNN) decoder \cite{arxiv:2401.06300}.'
     - 'Almost linear-time decoder \cite{arxiv:2411.02928}.'

codes/quantum/qubits/stabilizer/fermion_into_qubit/fermions_into_qubits.yml

@@ -18,7 +18,7 @@ description: |
 
   Subsequent encodings consisted of stabilizer codes with \(k < n\), ensuring anti-commutation through the long-range entanglement of the codestates.
   This makes it possible to reduce the Pauli weight of a Majorana operator by multiplying by a stabilizer.
-  Stabilizer constraints are often associated with loops of a 2D lattice.
+  For example, for stabilizer constraints associated with loops of a 2D lattice, applying loop constraints to high-weight fermionic string-like operators yields operators of lower weight.
 
   See \cite[Table I]{arxiv:2003.06939}\cite[Table I]{arxiv:2201.05153} for comparisons of various fermion-into-qubit codes.
   In addition to the children of this entry, various custom encodings exist \cite{arxiv:2009.11860,arxiv:2212.09731,arxiv:2311.07409,arxiv:2302.01862,doi:10.48550/arXiv.2403.17794} that can be tailored to the quantum simulation problem of interest.

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/toric/toric.yml

@@ -62,7 +62,7 @@ features:
 
   threshold:
     - 'The threshold under ML decoding with measurement errors corresponds to the value of a critical point of a three-dimensional random plaquette model \cite{arxiv:quant-ph/0110143,arxiv:quant-ph/0207088}.'
-    - '\(0.133\%\) for independent \(X,Z\) noise and faulty syndrome measurements using a cellular automaton decoder \cite{arxiv:1609.00510}.'
+    - '\(0.133\%\) for independent \(X,Z\) noise and faulty syndrome measurements using a local automaton decoder \cite{arxiv:1609.00510}.'
     - 'Toric-code thresholds for post-selected QEC can be studied with statistical mechanical models \cite{arxiv:2410.07598}.'
 
 realizations:

codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml

@@ -37,7 +37,8 @@ features:
   general_gates:
     - 'Logical \(CZ\), \(S\), and Hadamard gates when defined on a hypercubic lattice \cite{arxiv:2405.11719}.'
   decoders:
-    - 'Measurement-free local error correction circuit (LEC) using reinforcement learning \cite{arxiv:2408.09524}.'
+    - 'Local automaton decoder \cite{arxiv:1609.00510} based on Toom''s rule for the classical 2D repetition code \cite{manual:{A. L. Toom, “Nonergodic Multidimensional System of Automata”, Probl. Peredachi Inf., 10:3 (1974), 70–79; Problems Inform. Transmission, 10:3 (1974), 239–246},manual:{Toom, Andrei L. "Stable and attractive trajectories in multicomponent systems." Multicomponent random systems 6 (1980): 549-575.},doi:10.1007/978-1-4612-2168-5_18,doi:10.1147/rd.481.0005}.'
+    - 'Local automaton decoder obtained from reinforcement learning \cite{arxiv:2408.09524}.'
   code_capacity_threshold:
     - 'Independent \(X,Z\) noise: \(2.117\%\) with Hastings decoder \cite{arxiv:1609.00510} and \(7.3\%\) with RG decoder for 4D surface code \cite{arxiv:1708.09286}.
     It is conjectured via a statistical-mechanical mapping that the optimal ML decoder yields a threshold of \(11.003\%\) \cite{arxiv:hep-th/0310279}.'