@@ -34,7 +34,7 @@ features:
     Bounds exist on the one-shot capacity, i.e., the achievability of classical codes given only one use of the quantum channel.
     The ideal decoding error is suppressed exponentially with the number of subsystems \(n\) (for c-q block codes), and the achievable exponent has been studied in Refs. \cite{arxiv:quant-ph/9703013,arxiv:quant-ph/9907087,arxiv:quant-ph/0206186,arxiv:quant-ph/0611013,arxiv:0805.4092,arxiv:1007.5456,arxiv:1312.3822,arxiv:2208.02132,arxiv:2303.04138,arxiv:2310.09014}; see \cite[Table 2]{arxiv:2208.02132} for a summary.
     Achievable error exponents for communication are related to those for privacy amplification \cite{arxiv:2207.08899}.
-    In the high-rate case, a lower \cite{arxiv:1201.5411} and upper \cite{arxiv:2407.12403} bound on the error exponent for general channels matches a conjecture by Holevo \cite{arxiv:quant-ph/9907087}.
+    In the high-rate case, an upper \cite{arxiv:1201.5411} and a lower \cite{arxiv:2407.11118,arxiv:2407.12403} bound on the error exponent for general channels coincide, and the lower bound proves a conjecture by Holevo \cite{arxiv:quant-ph/9907087}.
     A one-shot bound for random codes \cite{arxiv:2507.06232} resolves a conjecture by Burnashev and Holevo \cite{arxiv:quant-ph/9703013}. 
 
     Unambiguous state discrimination (USD) can be used to achieve Holevo capacity on a general pure-state c-q channel \cite{doi:10.1109/ISIT.2013.6620209}.
@@ -52,6 +52,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -22,6 +22,7 @@ features:
     - 'Universal topological quantum computation is possible for certain groups such as \(G=D_3=S_3\) \cite{arxiv:quant-ph/0306063,arxiv:0901.1345}.'
     - 'For \(G=S_3\), Ref. \cite{arxiv:1401.7096} gives measurement-assisted universal gate sets; circuit-level fault tolerance can be improved using an anyon interferometer \cite{arxiv:2411.09697}.'
   code_capacity_threshold:
+    - 'For \(G=S_3\), the submodel restricted to the \(\Phi\) and \(\Lambda\) anyons has a threshold of about \(7\%\) total error probability per spin \cite{arxiv:1310.3846}.'
     - 'Behavior under \(X\)-type noise (namely, diffusion of certain anyons) for the \(G=D_4\) case is related to the phase diagram of a disordered net model \cite{arxiv:2409.12948}.'
 
   fault_tolerance:
@@ -50,6 +51,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -14,7 +14,7 @@ alternative_names:
   - 'Superposition of coherent states (SCS)'
 
 description: |
-  Rotation-symmetric bosonic Fock-state code encoding a \(q\)-dimensional qudit into one oscillator which utilizes a constellation of \(q(S+1)\) coherent states distributed equidistantly around a circle in phase space of radius \(\alpha\).
+  Rotation-symmetric bosonic Fock-state code encoding a \(q\)-dimensional qudit into one oscillator which utilizes a constellation of \(q(S+1)\) coherent states distributed equidistantly around a circle in phase space of radius \(\alpha\) \cite{arxiv:1605.00357}.
 
   Codewords for a qubit code (\(q=2\)) consist of a coherent state \(|\alpha\rangle\) projected onto a subspace of Fock state number modulo \(2(S+1)\). The logical state \(|\overline{0}\rangle\) is in the \(\{|0\rangle , |2(S+1)\rangle , |4(S+1)\rangle \cdots \}\) Fock-state subspace, while \(|\overline{1}\rangle\) is in the \(\{|(S+1)\rangle, |3(S+1)\rangle , |5(S+1)\rangle , |7(S+1)\rangle \cdots \}\) subspace.
   These projected coherent states make up generalized cat states \cite{doi:10.1016/0031-8914(74)90215-8,doi:10.1007/BF02581033}. 
@@ -67,6 +67,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -35,6 +35,7 @@ protection: 'For stabilizers \(\hat{S}_q(2\alpha),\hat{S}_p(2\beta)\), the code
 features:
   encoders:
     - 'Dissipative stabilization of finite-energy square-lattice GKP states using stabilizers conjugated by a \textit{cooling} \cite[Appx. B]{arxiv:1310.7596} or \textit{damping} operator, i.e., a damped exponential of the total occupation number \cite{arxiv:2009.07941,arxiv:2010.09681}. Preparation of approximate square-lattice GKP states has been studied both theoretically and experimentally \cite{arxiv:1506.05033,arxiv:1709.08580,arxiv:1907.12487,arxiv:1910.03673}. Various damped versions of GKP states are equivalent \cite{arxiv:1910.08301,arxiv:2012.12488}, and there exists a Fock-state expansion \cite[Appx. A]{arxiv:2002.11008}.'
+    - 'Heralded preparation from a squeezed state using one ancilla qubit, by repeated qubit-controlled displacements of doubling length, each followed by a qubit measurement \cite{arxiv:quant-ph/0205114}.'
     - 'Two Josephson junctions coupled by a gyrator \cite{arxiv:2002.07718}.'
     - 'Periodic driving (a.k.a. Floquet engineering) \cite{arxiv:2303.03541}.'
     - 'Approximate GKP states can be prepared using Gaussian operations and photon detectors \cite{arxiv:1902.02323}.'
@@ -94,6 +95,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -37,7 +37,7 @@ features:
   general_gates:
     - 'Gaussian operations and homodyne measurements on non-magic GKP states are classically simulable \cite{arxiv:2406.06418}, and there is a sufficient condition for an additional element to achieve universal quantum computation \cite{arxiv:2309.07820}. There is an algorithm for GKP circuit simulation whose runtime scales with the amount of negativity of the Zak-Gross Wigner function \cite{arxiv:2412.13136}.'
     - 'There is a relation between magic (i.e., how far away a state is from being a stabilizer state) and non-Gaussianity for GKP codewords \cite{arxiv:2109.13018,arxiv:2406.06418}. In particular, implementing a non-Clifford logical gate requires a higher degree of non-Gaussianity than that expressed by ideal non-normalizable GKP states \cite{arxiv:2406.06418}.'
-    - 'By applying GKP error correction to Gaussian input states, computational universality can be achieved without additional non-Gaussian elements  \cite{arxiv:1903.00012}. This procedure can be alternatively described as performing heterodyne detection on one half of a GKP encoded Bell pair. The cubic phase gate is not a suitable gate \cite{arxiv:2009.05309}.'
+    - 'By applying GKP error correction to Gaussian input states, computational universality can be achieved without additional non-Gaussian elements  \cite{arxiv:1903.00012}. This procedure can be alternatively described as performing heterodyne detection on one half of a GKP encoded Bell pair. The cubic phase gate is not a suitable gate for unbiased GKP states \cite{arxiv:2009.05309}. With on-demand noise biasing before the gate, the logical error of the cubic-phase \(T\) gate vanishes as GKP squeezing increases \cite{arxiv:2511.20355}.'
     - 'Logical shadow tomography protocol \cite{arxiv:2411.00235}.'
     - 'Some gates have a constant logical gate error even in the limit of infinite squeezing \cite{arxiv:2509.14658}.'
 
@@ -74,6 +74,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: JonathanConrad
 
@@ -89,14 +89,14 @@ protection: |
   Given some code defined by projector \(\Pi = U U^\dagger\), \(\Pi\) is \textit{\(\epsilon\)-correctable}
   with respect to some noise channel \(\mathcal{E}\) if
   \begin{align}
-    \Pi E_i^{\dagger}E_j \Pi =\lambda_{ij}\Pi +\Pi B_{ij}\Pi ~,
+    \Pi E_j^{\dagger}E_i \Pi =\lambda_{ij}\Pi +\Pi B_{ij}\Pi ~,
   \end{align}
   where \(\Lambda(\rho)=\mathrm{Tr}(\rho)\sum_{ij} \lambda_{ij}|i\rangle\langle j|\)
   is a density operator,
   \begin{align}
     (\Lambda+B)(\rho)=\Lambda(\rho)+\sum_{ij}\mathrm{Tr}(\rho B_{ij})|i\rangle\langle j|
   \end{align}
-  is the output state of the complementary noise channel \(\mathcal{E}^C = \Lambda+B\), and the Bures distance \(d(\Lambda+B,\Lambda)\le\epsilon\)~\cite{arxiv:0907.5391}.
+  is the output state of the complementary noise channel \(\mathcal{E}^C = \Lambda+B\), and the Bures distance \(d(\Lambda+B,\Lambda)\le\epsilon\)~\cite{arxiv:0907.5391,arxiv:2607.22995}.
   An alternative measure, the \textit{AQEC relative entropy}, measures the relative entropy between \(\Lambda + B\) and \(\Lambda\) \cite{arxiv:2312.16991}.
   The non-correctable contributions \(B_{ij}\) can be arranged in a signature vector that is amenable to numerical optimization in the space of Stiefel manifolds \cite{arxiv:2410.07983,arxiv:2504.20847}. 
   The Frobenius norm of the matrix \(B_{ij}\) bounds the difference between the two \hyperref[topic:quantum-weight-enumerator]{quantum weight enumerators} \cite{arxiv:2108.04434}.
@@ -197,6 +197,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: M10T
 
@@ -122,7 +122,7 @@ features:
       However, only a finite-depth circuit and one round of measurements is required for non-Abelian topological orders with a Lagrangian subgroup \cite{arxiv:2209.03964}.
     - 'Algorithm that takes in reduced density matrices and outputs a circuit preparing the global state in polynomial time \cite{arxiv:2410.23544}.'
   general_gates:
-    - 'Ising anyon braiding and fusion were studied in a phenomenological model that was the first to study error correction with non-Abelian anyons \cite{arxiv:1311.0019}.'
+    - 'Error correction with non-Abelian anyons was first studied concurrently for Ising anyon braiding and fusion in a phenomenological model \cite{arxiv:1311.0019} and for the \(D(S_3)\) quantum double \cite{arxiv:1310.3846}.'
     - 'Codes with non-Abelian anyons present two complications. First, their anyons are not always represented as tensor-product unitary operators and thus cannot be corrected by such operations. Second, fusing such anyons can yield more than one outcome, complicating decoding algorithms \cite{arxiv:hep-th/0110205}.'
 
 
@@ -152,6 +152,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-10-11'
     - user_id: VictorVAlbert
 
@@ -129,7 +129,7 @@ features:
     - |
       Computing with \hyperref[topic:clifford]{Clifford gates}, Pauli measurements, and classical feedforward acting on stabilizer states only can be efficiently simulated on a classical computer by tracking stabilizer and logical generators, according to the \textit{Gottesman-Knill theorem} \cite{arxiv:quant-ph/9807006,preset:KnillPC98}.
       There is a canonical form for \hyperref[topic:clifford]{Clifford circuits} \cite{arxiv:2003.09412,arxiv:2408.15202} and many algorithms for simulating them \cite{arxiv:quant-ph/0406196,arxiv:1712.03554,arxiv:2301.02356}.
-      Universal quantum computing can be achieved using \hyperref[topic:clifford]{Clifford gates} and a single type of \hyperref[topic:clifford]{non-Clifford} gate, such as the \(T\) gate \cite{arxiv:quant-ph/9503016}.
+      Universal quantum computing can be achieved using \hyperref[topic:clifford]{Clifford gates} and a single type of \hyperref[topic:clifford]{non-Clifford} gate, such as the \(T\) gate \cite{arxiv:quant-ph/9906054}.
       More generally, the \textit{Solovay-Kitaev} theorem \cite{doi:10.1070/RM1997v052n06ABEH002155,doi:10.1090/gsm/047} states that any subset of gates that generates a dense subgroup of the full \(n\)-qubit gate group can be used to construct any gate to arbitrary accuracy (see \cite{arxiv:quant-ph/0505030}\cite[Appx. 3]{doi:10.1017/cbo9780511976667.019}). The task of approximating a desired gate by \hyperref[topic:clifford]{Clifford gates} and a fixed set of \hyperref[topic:clifford]{non-Clifford} gates is called \textit{gate compilation} or \textit{circuit synthesis}.
     - 'Non-Clifford gates are typically more difficult to implement than \hyperref[topic:clifford]{Clifford gates} and so are treated as a resource. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}. There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189,arxiv:1011.2497}.'
     - |
@@ -174,7 +174,7 @@ features:
         When different classes of circuit locations have different error rates, the single-number threshold generalizes to a \textit{threshold surface} in the space of error-rate vectors. A one-level crossing where a particular logical location becomes more reliable is then not a full-fledged threshold for the entire circuit; deciding whether a protocol really improves may require following the coupled recurrence relations through additional concatenation levels \cite[Sec. 14.7.6]{preset:GottesmanBook}.
         Fault-tolerant computations with no notion of locality can be made local on a 2D or 3D geometry with minimal overhead \cite{arxiv:2402.13863}.
         \end{defterm}
-    - 'There is an upper bound on the threshold under local update recovery that is derived via quantum optimal transport \cite{arxiv:quant-ph/0310136} (see also Ref. \cite{arxiv:2309.16241}).'
+    - 'The threshold noise rate is at most \(1/2\), assuming \(\mathsf{QP}\not\subseteq\mathsf{QNC}^1\) \cite{arxiv:quant-ph/0310136}. See Ref. \cite{arxiv:2309.16241} for an upper bound on the threshold under local update recovery derived via quantum optimal transport.'
     - 'There is a threshold against depolarizing noise for any single-qubit gate that determines if the gate enables universal quantum computation \cite{arxiv:0907.3189,arxiv:1011.2497}.'
     - '\begin{defterm}{Measurement threshold}
       \label{topic:measurement-threshold}
@@ -210,7 +210,7 @@ relations:
       detail: |
         Computing with \hyperref[topic:clifford]{Clifford gates}, Pauli measurements, and classical feedforward acting on stabilizer states only can be efficiently simulated on a classical computer by tracking stabilizer and logical generators, according to the \textit{Gottesman-Knill theorem} \cite{arxiv:quant-ph/9807006,preset:KnillPC98}.
         There is a canonical form for \hyperref[topic:clifford]{Clifford circuits} \cite{arxiv:2003.09412,arxiv:2408.15202} and many algorithms for simulating them \cite{arxiv:quant-ph/0406196,arxiv:1712.03554,arxiv:2301.02356}.
-        Universal quantum computing can be achieved using \hyperref[topic:clifford]{Clifford gates} and a single type of \hyperref[topic:clifford]{non-Clifford} gate, such as the \(T\) gate \cite{arxiv:quant-ph/9503016}.
+        Universal quantum computing can be achieved using \hyperref[topic:clifford]{Clifford gates} and a single type of \hyperref[topic:clifford]{non-Clifford} gate, such as the \(T\) gate \cite{arxiv:quant-ph/9906054}.
         More generally, the \textit{Solovay-Kitaev} theorem \cite{doi:10.1070/RM1997v052n06ABEH002155,doi:10.1090/gsm/047} states that any subset of gates that generates a dense subgroup of the full \(n\)-qubit gate group can be used to construct any gate to arbitrary accuracy (see \cite{arxiv:quant-ph/0505030}\cite[Appx. 3]{doi:10.1017/cbo9780511976667.019}). The task of approximating a desired gate by \hyperref[topic:clifford]{Clifford gates} and a fixed set of \hyperref[topic:clifford]{non-Clifford} gates is called \textit{gate compilation} or \textit{circuit synthesis}.
     - code_id: qubit_classical_into_quantum
       detail: 'Qubit c-q codes are qubit codes designed to transmit classical information.'
@@ -220,6 +220,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-09-28'
     - user_id: VictorVAlbert
 
@@ -25,7 +25,8 @@ features:
     - 'Encoding circuits can be viewed as matrix-product-state tensor networks \cite{arxiv:1312.4578}.'
   decoders:
     - 'Quantum Viterbi decoder \cite{arxiv:quant-ph/9806032,arxiv:quant-ph/0304189,arxiv:quant-ph/0401134}.'
-    - 'ML decoder \cite{arxiv:quant-ph/0304189}.'
+    - 'Decoder finding the most likely error over any memoryless channel \cite{arxiv:quant-ph/0304189}.'
+    - 'Degenerate Viterbi decoder, which finds the most likely class of degenerate errors in time linear in the number of qubits \cite{arxiv:1204.2439}.'
 
 notes:
   - 'See Refs. \cite{arxiv:quant-ph/0304189,arxiv:quant-ph/0511016,arxiv:quant-ph/0602129,arxiv:quant-ph/0703181} for explicit and simple examples.'
@@ -53,6 +54,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -15,9 +15,9 @@ description: |
   (contrasting with the weight-six checks of standard BB codes), designed and
   benchmarked for long chains of trapped ions \cite{arxiv:2503.22071}.
 
-  Two highlighted instances are \([[30,4,5]]\) and \([[48,4,7]]\), which improve
-  the best-known BB6 distances at the same \([[n,k]]\): respectively
-  \([[30,4,4]]\) and \([[48,4,6]]\) \cite{arxiv:2503.22071}.
+  Two highlighted instances are \([[30,4,5]]\) and \([[48,4,7]]\) \cite{arxiv:2503.22071}.
+  Their distances exceed those of BB6 codes with the polynomial form of Ref. \cite{arxiv:2308.07915} at the same \([[n,k]]\), namely \([[30,4,4]]\) and \([[48,4,6]]\) \cite{arxiv:2503.22071}.
+  Other BB6 codes reach \([[30,4,6]]\) \cite{arxiv:2408.10001}.
 
 features:
   fault_tolerance:
@@ -34,6 +34,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert