single shot refs

codes/quantum/properties/block/single_shot.yml

@@ -6,16 +6,23 @@
 code_id: single_shot
 
 name: 'Single-shot code'
-introduced: \cite{arxiv:1404.5504}
+introduced: \cite{arxiv:1404.5504,arxiv:1805.09271}
 
 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 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.
 
-  The single-shot property usually 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.
+  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.
+
 
 # In other words, the single-shot property implies that the number of error-correcting rounds necessary for successful error correction is independent of the number of subsystems \(n\).
 

codes/quantum/qubits/stabilizer/qldpc/homological/quantum_expander.yml

@@ -32,6 +32,8 @@ features:
 relations:
   parents:
     - code_id: hypergraph_product
+    - code_id: single_shot
+      detail: 'Quantum expander codes are single-shot \cite{arxiv:1808.03821}.'
   cousins:
     - code_id: expander
 #      detail: 'Quantum expander codes are constructed from classical expander codes.'

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -104,6 +104,7 @@ features:
     - 'Homomorphic gadgets fault-tolerant measurement unify Steane and Shor error correction \cite{arxiv:2211.03625}.'
     - 'Parallel syndrome extraction for distance-three codes can be done fault-tolerantly using one flag qubit \cite{arXiv:2208.00581}.'
     - 'Distance-preserving flag fault-tolerant error correction using lookup tables for small codes \cite{arxiv:2306.12862}.'
+    - 'A fault-tolerant error-correction protocol using \(O(d\log d)\) syndrome measurements can be applied to any CSS code with distance \(d \geq \Omega(n^{\alpha})\) for any \(\alpha > 0\) \cite{arxiv:2002.05180}.'
   code_capacity_threshold:
     - 'Bounds on code capacity thresholds for various noise models exist in terms of stabilizer generator weights \cite{arxiv:1208.2317,arxiv:1412.6172}.'
   decoders:
@@ -144,6 +145,9 @@ relations:
     - code_id: ag
       detail: 'Algebraic geometry codes can be plugged into the CSS construction to yield asymptotically good quantum codes \cite{arxiv:quant-ph/0006061}.'
 
+# - code_id: single_shot
+# detail: 'A fault-tolerant error-correction protocol using \(O(d\log d)\) syndrome measurements can be applied to any CSS code with distance \(d \geq \Omega(n^{\alpha})\) for any \(\alpha > 0\) \cite{arxiv:2002.05180}. This implies that the single-shot property is not necessary to reduce the number of error-correction rounds required for fault tolerance.'
+
 
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 _meta:

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

@@ -49,7 +49,6 @@ features:
     - '\(\geq 6.25\%\) threshold for 2D color codes with error-free syndrome extraction, and \(0.1\%\) with faulty syndrome extraction \cite{arXiv:0907.1708}.'
     - '\(0.46\%\) for 3D codes with clustering decoder \cite{arXiv:1708.07131}.'
     - '\(1.9\%\) for 1D string-like logical operators and \(27.6\%\) for 2D sheet-like operators for 3D codes with noise models using optimal decoding and perfect measurements \cite{arXiv:1708.07131}.'
-    - '\(0.31\%\) noise threshold error rate for gauge code using clustering decoder \cite{arXiv:1503.08217}.'
     - '\(0.2\%\) with depolarizing circuit-level noise using two flag-qubits per stabilizer generator and the restriction decoder \cite{arXiv:1911.00355}.'
     - '\(0.143\%\) with depolarizing circuit-level noise using perfect-matching decoder \cite{arXiv:1407.5103}.'
     - '\(>0\%\) threshold with sweep decoder \cite{doi:10.7907/059V-MG69}.'

codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml

@@ -18,7 +18,7 @@ relations:
   parents:
     - code_id: subsystem_stabilizer
     - code_id: single_shot
-      detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621}.'
+      detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621,arxiv:2305.06365}.'
   cousins:
     - code_id: 3d_surface
     - code_id: self_correct

codes/quantum/qubits/subsystem/topological/subsystem_color.yml

@@ -10,17 +10,27 @@ logical: qubits
 name: 'Subsystem color code'
 introduced: '\cite{arxiv:0908.4246,arxiv:1311.0879}'
 
+alternative_names:
+  - 'Gauge color code'
+
 description: |
   Stub.
 
+features:
+  decoders:
+    - '\(0.31\%\) noise threshold error rate using clustering decoder \cite{arXiv:1503.08217}.'
+
+
 relations:
   parents:
     - code_id: subsystem_stabilizer
+    - code_id: single_shot
+      detail: 'The subsystem color code is a single-shot code \cite{arxiv:1503.08217}.'
   cousins:
     - code_id: color
     - code_id: symmetry_protected_self_correct
       detail: 'A particular gauge-fixed version of this code on a 3D lattice yields a self-correcting memory protected by one-form symmetries (see Sec. IV D of Ref. \cite{arXiv:1805.01474}). The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length.
-      The gauge color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.'
+      The subsystem color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.'
 
 
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