~

codes/quantum/qubits/majorana/majorana_stab.yml

@@ -46,7 +46,7 @@ relations:
     - code_id: dual
       detail: 'Classical self-orthogonal codes can be used to construct Majorana stabilizer codes \cite{arxiv:1703.00459}. The direct relationship between the two codes follows from expressing the Majorana strings as binary vectors – akin to the \hyperref[topic:binary-symplectic-representation]{symplectic representation} – and observing that the binary stabilizer matrix \(S\) for such a Majorana stabilizer code satisfies \(S\cdot S^T=0\) because it has commuting stabilizers, which is precisely the condition \(G\cdot G^T=0\) on the generator matrix \(G\) of a self-orthogonal classical code. A self-orthogonal classical code \(C\) with parameters \([2N,k,d]\) yields a Majorana stabilizer code with parameters \([[N,N-k,d^\perp]]_f\), where \(d^\perp\) is the code distance of the dual code \(C^\perp\).'
     - code_id: qubit_css
-      detail: 'Every \([[n,k,d]]_f) Majorana stabilizer code is associated with a \([[2n,2k,d]]\) self-dual qubit CSS code \cite[Lemma 2]{arxiv:1004.3791}.'
+      detail: 'Every \([[n,k,d]]_f\) Majorana stabilizer code is associated with a \([[2n,2k,d]]\) self-dual qubit CSS code \cite[Lemma 2]{arxiv:1004.3791}.'
     - code_id: binary_linear
       detail: 'When constructing a Majorana stabilizer code from a self-orthogonal classical code with an odd number of bits and generator matrix \(G\), a more complex procedure must be applied to ensure that the fermion code has an even number of Majorana zero modes, and thus a physical Hilbert space \cite{arxiv:1004.3791,arxiv:1703.00459}. Rather than taking \(G\) to be the stabilizer matrix as in the even case, we take \(G\oplus G\). This is a concatenation of classical codes as in the CSS construction and it yields a mapping \([2n-1,k,d]\rightarrow [[2n-1,2n-1-k,d^\perp]]_f\). This procedure may be further generalized by concatenating two different self-orthogonal classical codes with an odd number of bits, as is often done in the CSS construction.'
     - code_id: binary_cyclic

codes/quantum/qubits/stabilizer/magic/k-divisible/quantum_h.yml

@@ -12,7 +12,7 @@ short_name: '\([[k+4,k,2]]\)'
 introduced: '\cite{arxiv:1210.3388}'
 
 description: |
-  Family of \([[k+4,k,2]]\) CSS codes (for even \(k\)) with transversal Hadamard gates that are relevant to magic state distillation.
+  Family of \([[k+4,k,2]]\) self-dual CSS codes (for even \(k\)) with transversal Hadamard gates that are relevant to magic state distillation.
   The four stablizer generators are \(X_1X_2X_3X_4\), \(Z_1Z_2Z_3Z_4\), \(X_1X_2X_5X_6...X_{k+4}\), and \(Z_1Z_2Z_5Z_6...Z_{k+4}\).'
 
 protection: 'Detects weight-one Pauli errors. The \(r\)-level contatenated H code detects weight Pauli errors up to weight \(2^r-1\).'