~

codes/quantum/oecc.yml

@@ -29,7 +29,7 @@ protection: |
   where \(\Pi\) is a projector onto the codespace \(\mathsf{C}\), and \(g_{ab}^{\mathsf{B}}\) is an arbitrary operator on the gauge subsystem.
   These have also been studied in the presence of continuous noise \cite{arxiv:0806.3145}.
 
-  A \textit{unitarily correctable subsystem} is a subsystem code whose encoded information can be recovered via a unitary, i.e., without measurement \cite{arxiv:quant-ph/0608045}. For unital noise channels, such codes are related to the multiplicative domain of the channel \cite{arxiv:0811.0947}.
+  A \textit{unitarily correctable subsystem} is a subsystem code whose encoded information can be recovered via a unitary, i.e., in a measurement-free way \cite{arxiv:quant-ph/0608045}. For unital noise channels, such codes are related to the multiplicative domain of the channel \cite{arxiv:0811.0947}.
 
 features:
   encoders:

codes/quantum/properties/asymmetric_qecc.yml

@@ -78,6 +78,8 @@ relations:
       detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4,arxiv:0804.4316}, including subsystem BCH codes \cite{arxiv:0803.0764}.'
     - code_id: pg_ldpc
       detail: 'FG-LDPC codes can be used to construct asymmetric CSS codes \cite[Lemma 4.1]{doi:10.1098/rspa.2008.0439}\cite{arxiv:0804.4316}.'
+    - code_id: hermitian
+      detail: 'Hermitian codes can be used to construct asymmetric Galois-qudit CSS codes \cite{arxiv:1102.3605}.'
     - code_id: galois_polynomial
       detail: 'Asymmetric Galois-qudit RS codes have been constructed \cite{manual:{La Guardia, G. G., R. Palazzo, and C. Lavor. "Nonbinary quantum Reed-Solomon codes." Int. J. Pure Applied Math 65.1 (2010): 55-63.},doi:10.1007/s11128-011-0269-3}.'
     - code_id: bacon_shor
@@ -93,6 +95,8 @@ relations:
       detail: 'QSC code parameters against loss/gain errors and Gaussian rotations can be tuned.'
     - code_id: quantum_parity
       detail: 'QPC parameters against bit- and phase-noise can be tuned.'
+    - code_id: eastab
+      detail: 'Entanglement can help decode asymmetric quantum codes \cite{arxiv:1104.5004}.'
 
 
 

codes/quantum/properties/hamiltonian/self_correct.yml

@@ -40,7 +40,7 @@ protection: |
 
   An \(n\)-dependent energy barrier to creating all logical errors is likely necessary for a thermally stable memory, having been shown as such for a large class of 2D topological phases \cite{arxiv:0810.3557,arxiv:1412.2858,arxiv:1601.01324,arxiv:2107.01628}.
   Two-dimensional stabilizer codes \cite{arxiv:0810.1983} and encodings of frustration-free code Hamiltonians \cite{arxiv:1209.5750} admit only constant-energy excitations, and so do not have admit such a barrier.
-  No-go theorems for 3D models are much more restrictive, e.g., a 3D lattice stabilizer code with a locality-preserving non-Clifford gate cannot have a microscopic energy barrier \cite{arxiv:1408.1720}.
+  No-go theorems for 3D models are much more restrictive \cite{arxiv:1105.4159}, e.g., a 3D lattice stabilizer code with a locality-preserving non-Clifford gate cannot have a microscopic energy barrier \cite{arxiv:1408.1720}.
   There exist several candidates for self-correction as well as several partially self-correcting memories (see cousins below).
 
 

codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml

@@ -19,7 +19,7 @@ features:
   decoders:
     - 'Renormalization group (RG) decoder \cite{arxiv:1006.1362}.'
     - 'Tensor-network based decoder for 2D codes subject to correlated noise \cite{arxiv:1809.10704}.'
-    - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2401.06300,arxiv:2402.14906}.'
+    - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2401.06300,arxiv:2402.14906}; see also Refs. \cite{arxiv:0911.3843,arxiv:1107.3940}.'
   code_capacity_threshold:
     - 'Noise thresholds can be formulated as anyon \hyperref[topic:code-switching]{condensation} transitions in a topological field theory \cite{arxiv:2301.05687}, generalizing the mapping of the effect of noise on a code state to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}.
     Namely, the noise threshold for a noise channel \(\cal{E}\) acting on a 2D stabilizer state \(|\psi\rangle\) can be obtained from the properties of the resulting (mixed) state \(\mathcal{E}(|\psi\rangle\langle\psi|)\) \cite{arxiv:2301.05238,arxiv:2301.05687,arxiv:2301.05689,arxiv:2309.11879, arxiv:2401.17359}.'

codes/quantum/qubits/small_distance/small/steane/steane.yml

@@ -67,6 +67,9 @@ features:
     - 'Fault-tolerant logical zero and magic state preparation \cite{doi:10.1038/srep19578}. Magic-state preparation converts unbiased noise into biased noise \cite{arxiv:2401.10982}.'
     - 'Pieceable fault-tolerant CCZ gate \cite{arxiv:1603.03948}.'
 
+  decoders:
+    - 'Shor error correction fidelity calculation \cite{arxiv:1101.1950}.'
+
   fault_tolerance:
     - 'A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[15,1,3]]\) code \cite{arxiv:1304.3709,arxiv:1403.2734,arxiv:1703.03860,arxiv:2210.14074}.'
     - 'A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'

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

@@ -172,7 +172,7 @@ relations:
     - code_id: hamiltonian
       detail: 'While codewords of the surface code form ground states of the code''s stabilizer Hamiltonian, they can also be ground states of other gapless Hamiltonians \cite{arxiv:1111.5817}.'
     - code_id: self_correct
-      detail: 'Various candidates for self-correcting quantum memories have been constructed by coupling neighboring anyons so as to prevent them from spreading \cite{arxiv:0812.4622,arxiv:0908.4264,arxiv:1406.2338,arxiv:1512.04528}'
+      detail: 'Various candidates for self-correcting quantum memories have been constructed by coupling neighboring anyons so as to prevent them from spreading \cite{arxiv:0812.4622,arxiv:0908.4264,arxiv:1101.6028,arxiv:1406.2338,arxiv:1512.04528}'