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codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -78,7 +78,7 @@ protection: |
 # A stabilizer code is \textit{geometrically local} if the support of the stabilizer generators is bounded by a ball of size independent of \(n\).
 
 features:
-  rate: 'The \textit{hashing bound} states that there is a qubit stabilizer code achieving a rate \(R = 1 - H(\mathbf{p})\) for a Pauli noise channel with Pauli error probabilities \(\mathbf{p}=(p_I,p_X,p_Y,p_Z)\), where \(H(\mathbf{p})\) is the entropy of the argument \cite[Thm. 23.6.2]{doi:10.1017/CBO9781139525343}.'
+  rate: 'The \textit{hashing bound} states that there is a qubit stabilizer code achieving a rate \(R = 1 - H(\mathbf{p})\) for a Pauli noise channel with Pauli error probabilities \(\mathbf{p}=(p_I,p_X,p_Y,p_Z)\), where \(H(\mathbf{p})\) is the entropy of the argument \cite[Thm. 23.6.2]{doi:10.1017/CBO9781139525343}. Finite block length bounds and a refinement of the hashing bound have been developed \cite{arxiv:2408.15202}.'
   encoders:
     - |
       Clifford circuits, i.e., those consisting of CNOT, Hadamard, and certain phase gates, using an algorithm \cite{arxiv:2301.02356} based on the Gottesman-Knill theorem \cite{arxiv:quant-ph/0406196} or using ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725} (with the latter providing a unique decomposition \cite{arxiv:2406.12083}).