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codes/quantum/properties/block/single_shot.yml

@@ -12,13 +12,13 @@ description: |
   Measurement errors during decoding can yield the wrong syndrome outcome, which can cause error correction to fail even against correctable data errors.
   A single-shot code is a block quantum code admitting a fault-tolerant error-correcting protocol that does not "fail too badly" when faced with noisy syndrome measurements.
 
-  The property typically implies that a sufficiently large number of error-correction rounds will keep both data and measurement errors bounded, as opposed to causing to eventually become uncorrectable.
+  The property typically implies that a sufficiently large number of error-correction rounds will keep both data and measurement errors bounded, as opposed to yielding eventually uncorrectable residual errors.
   The property is sufficient (but not necessary \cite{arxiv:2002.05180}) to reduce the number of error-correction rounds required for fault-tolerant error correction.
 
   In the loosest form of the single-shot property for qubit, modular qudit, or Galois qudit codes, given some data error \(e\), ideal data error syndrome \(s\), and measurement error \(m\), there exists an error-correction protocol that outputs a correction \(f\) such that the Hamming weight of the residual error  after correction, \(e+f\), is \textit{polynomial} in the weight of \(m\).
   Note that the \textit{stabilizer-reduced weight} \cite{arxiv:1805.09271} of \(e\) is often used instead of the weight of \(e\), with the justification that many decoders are desgined to obtain the minimum-weight error representative.
 
-  Typical noise models considered include stochastic noise \cite{arxiv:1404.5504} and adversarial noise \cite{arxiv:1805.09271}.
+# Typical noise models considered include stochastic noise \cite{arxiv:1404.5504} and adversarial noise \cite{arxiv:1805.09271}.
 
 #  This can happen for some QLDPC codes and some abelian topological codes.
 #   The property is named after its primary implication, namely, that one can obtain fault-tolerant syndrome data from only a single round of error correction.