refs

codes/classical/analog/analog.yml

@@ -77,6 +77,9 @@ relations:
     - code_id: block
     - code_id: group_classical
       detail: 'Sphere-packing alphabets \(\mathbb{R}^n\) are infinite fields, which are groups under addition.'
+  cousins:
+    - code_id: hamiltonian
+      detail: 'The Cohn-Elkies linear programming bound is related to the conformal bootstrap, which is a way of utilizing symmetry to constrain correlation functions of conformal field theories \cite{arxiv:1905.01319}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/css/quantum_parity.yml

@@ -42,7 +42,7 @@ protection: 'Has distance \(d=\min(m_1,m_2)\).'
 
 features:
   encoders:
-    - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294} and tree tensor networks \cite{arxiv:1312.4578}.'
+    - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294,arxiv:2409.13801} and tree tensor networks \cite{arxiv:1312.4578}.'
     - 'Linear-optical encoding \cite{arxiv:0707.0903}.'
   decoders:
     - 'Teleportation-based QEC \cite{arxiv:1310.5291}.'

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -129,6 +129,7 @@ features:
   decoders:
     - 'The size of the circuit extracting the syndrome depends on the weight of its corresponding stabilizer generator. Syndrome extraction circuits can be simulated efficiently using dedicated software (e.g., STIM \cite{arxiv:2103.02202}) and there are many general schemes for generating them \cite{arxiv:2408.01339} (see also \cite{arxiv:2402.04093}).'
     - 'DiVincenzo-Aliferis syndrome extraction circuits \cite{arxiv:quant-ph/0607047}.'
+    - 'Greedy syndrome measurement schedule \cite{arxiv:2409.14283}.'
     - 'MPE decoding, i.e., the process of finding the most likely error, is \(NP\)-complete in general \cite{arxiv:1009.1319,manual:{Kuo, Kao-Yueh, and Chung-Chin Lu. "On the hardness of decoding quantum stabilizer codes under the depolarizing channel." 2012 International Symposium on Information Theory and its Applications. IEEE, 2012.}}. If the noise model is such that the most likely error is the lowest-weight error, then ML decoding is called \textit{minimum-weight} decoding. Maximum-likelihood (ML) decoding (a.k.a.\ degenerate maximum-likelihood decoding), i.e., the process of finding the most likely error class (up to degeneracy of errors), is \(\#P\)-complete in general \cite{arxiv:1310.3235}.'
     - 'Incorporating faulty syndrome measurements can be done by performing spacetime decoding, i.e., using data from past rounds for decoding syndromes in any given round. If a decoder does not process syndrome data sufficiently quickly, it can lead to the \textit{backlog problem} \cite{arxiv:1302.3428}, slowing down the computation.'
     - 'Splitting decoders \cite{arxiv:2309.15354}.'
@@ -157,6 +158,7 @@ features:
     - 'Fault-tolerant constant-depth unencoder transforming logical states into physical states using single-qubit measurements \cite{arxiv:2408.06299}.'
     - 'Post-selection based algorithm preparing magic state corresponding to arbitrary rotations \cite{arxiv:2303.17380}.'
     - '\hyperref[topic:code-switching]{Code switching} can be done using only transversal gates for qubit stabilizer codes \cite{arxiv:2409.13465}.'
+    - 'Flag-Proxy Networks (FPNs) \cite{arxiv:2409.14283}.'
 
   code_capacity_threshold:
     - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}. The AQEC relative entropy is related to the resulting threshold \cite{arxiv:2312.16991}.'

codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml

@@ -25,6 +25,8 @@ protection: |
 features:
   rate: 'In the double-cover construction \cite{arxiv:1301.6588}, an \(\{\ell,m\}\) input tiling yields a code family with an asymptotic rate of \(1 - 1/\ell - 1/m\).'
 
+  decoders:
+    - 'Two flag-based decoders \cite{arxiv:2409.14283}.'
 
 
 relations:

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

@@ -44,7 +44,7 @@ features:
 relations:
   parents:
     - code_id: surface
-      detail: 'The lattice of the rotated surface code can be obtained by taking the medial graph of the surface code lattice (treated as a graph) and applying a similar procedure to construct the check operators \cite{arxiv:quant-ph/0703272,arxiv:1606.07116}\cite[Fig. 8]{arxiv:2101.09349}. Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}.'
+      detail: 'The lattice of the rotated surface code can be obtained by taking the medial graph of the surface code lattice (treated as a graph) and applying a similar procedure to construct the check operators \cite{arxiv:quant-ph/0703272,arxiv:1606.07116}\cite[Fig. 8]{arxiv:2101.09349}. Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}. The rotated surface code presents certain savings over the original surface code \cite{arxiv:2409.14765}.'
     - code_id: quantum_tanner
       detail: 'Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}.'
     - code_id: hierarchical

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

@@ -31,6 +31,7 @@ features:
   decoders:
     - 'Due to the symmetries of hyperbolic surface codes, optimal measurement schedules of the stabilizers can be found \cite{arxiv:2010.09626}.'
     - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:1804.01950}.'
+    - 'Two flag-based decoders \cite{arxiv:2409.14283}.'
 
   code_capacity_threshold:
     - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:1805.00644}.'