~

codes/quantum/oscillators/stabilizer/hyperplane/analog_stabilizer.yml

@@ -43,6 +43,8 @@ relations:
       Protection of logical modes against small displacements cannot be done using only Gaussian resources \cite{arxiv:1810.00047,arxiv:quant-ph/0204052,arxiv:0811.3128}, so oscillator-into-oscillator GKP codes can be thought of as analog stabilizer encodings utilizing non-Gaussian GKP resource states.'
     - code_id: qudit_stabilizer
       detail: 'Prime-qudit stabilizer codes can be converted into analog stabilizer codes whose distance is at least as large as that of the original code \cite{arxiv:2303.17000}.'
+    - code_id: stab_8_3_3
+      detail: 'The eight-qubit Gottesman code has been extended to an analog stabilizer code \cite{arxiv:quant-ph/0405064}.'
 
 
 # Begin Entry Meta Information

codes/quantum/properties/stabilizer/stabilizer.yml

@@ -33,10 +33,8 @@ protection: |
 
 features:
   general_gates:
-    - 'The stabilizer formalism and Gottesman-Knill theorem have been extended to qubits, modular qudits, Galois qudits, and rotors \cite{arxiv:1210.3637,arxiv:1409.4800}.'
+    - 'A Gottesman-Knill-type theorem exists for qubits, modular qudits, Galois qudits, and rotors \cite{arxiv:1210.3637,arxiv:1409.4800}, as well as oscillators \cite{arxiv:quant-ph/0109047,arxiv:1210.1783,arxiv:1208.3660}.'
 
-
-features:
   decoders:
     - 'The structure of stabilizer codes allows for straightforward syndrome-based decoding because the stabilizer generators serve as the code''s check operators, and their eigenvalues serve as the error syndromes. The error correction process involves measuring the stabilizer generators and applying correcting Pauli-type operators based on the measurement outcomes.'
 

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -92,7 +92,7 @@ description: |
   \end{defterm}
 
   Alternative representations include the \textit{decoupling representation}, in which Pauli strings are represented as vectors over \(GF(2)\) using three bits \cite{arxiv:2305.17505}.
-  Qubit stabilizer states can be expressed in terms of linear and quadratic functions over \(\mathbb{Z}_2^n\) \cite{arxiv:quant-ph/0304125}.
+  Qubit stabilizer states can be expressed in terms of linear and quadratic functions over \(\mathbb{Z}_2^n\) \cite{arxiv:quant-ph/0304125,arxiv:0811.0898}.
 
 # More technically, let \(\phi\) be a bijection from a linear binary subspace to \(GF(4)^n\). Let \(C\) be a trace-Hermitian self-orthogonal additive subcode over \(GF(4)\), containing \(2^{n-k}\) vectors, such that there are no vectors of weight less than \(d\) in \(C^{\perp}\setminus C\). Then, any eigenspace of the inverse map \(\phi^{-1}(C)\) is an \([[n, k, d]]\) stabilizer code over \(GF(4)\).