quantum_ag

codes/quantum/qudits_galois/stabilizer/evaluation/binary_quantum_goppa.yml

@@ -10,9 +10,6 @@ logical: galois
 name: 'Quantum Goppa code'
 introduced: '\cite{arxiv:quant-ph/0006061,arxiv:quant-ph/0501074,doi:10.1007/s11128-006-0047-9}'
 
-alternative_names:
-  - 'Quantum AG code'
-
 description: |
   A Galois-qudit CSS code constructed using two Goppa codes.
   
@@ -31,29 +28,20 @@ description: |
 protection: 'Protects against weight \(t\) errors where \( 0 < t \leq  \lfloor \frac{d^*-g-1}{2} \rfloor \) where \( d^* = \text{deg} G + 2 -2g \) and \(g\) is the genus of the function field and \(d \geq n - \lfloor \frac{deg G}{2} \rfloor\). Such codes can exceed the \hyperref[topic:quantum-gv-bound]{quantum GV bound} \cite{doi:10.1007/s11128-006-0047-9}.'
 
 features:
-  rate: 'Quantum Goppa codes \cite{arxiv:quant-ph/0006061} and other quantum codes constructed from AG codes \cite{arxiv:quant-ph/0107129} can be asymptotically good. There exist three such families \cite{arxiv:2408.07764,arxiv:2408.09254,arxiv:2408.10140} that admit a diagonal transversal gate at the third level of the \term{Clifford hierarchy}.'
-
-  magic_scaling_exponent: 'By defining a generalization of triorthogonal matrices to Galois qudits of dimension \(q=2^m\), one can construct an asymptotically good family of quantum Goppa codes that admits a diagonal transversal gate at the third level of the \term{Clifford hierarchy} and attains a zero magic-state yield parameter, \(\gamma = 0\) \cite{arxiv:2408.07764}. This code can be treated as a qubit code by decomposing each Galois qudit into a Kronecker product of \(m\) qubits; see \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Two other such asymptotically good families exist \cite{arxiv:2408.09254,arxiv:2408.10140}, admitting a different diagonal gate at the third level of the \term{Clifford hierarchy}.'
-
+  rate: 'Quantum Goppa codes \cite{arxiv:quant-ph/0006061} can be asymptotically good.'
 
   encoders:
     - 'Encoding defined in Ref. \cite{arxiv:quant-ph/0107129} uses a technique from Ref. \cite{arxiv:quant-ph/0005008} to encode quantum stabilizer codes.'
 
-  transversal_gates:
-    - 'There exist three asymptotically good code families \cite{arxiv:2408.07764,arxiv:2408.09254,arxiv:2408.10140} that admit a diagonal transversal gate at the third level of the \term{Clifford hierarchy}.'
-
   decoders:
     - 'Farran algorithm \cite{arxiv:math/9910151}.'
 
 relations:
   parents:
-    - code_id: galois_css
-      detail: 'Goppa codes can be realized in the CSS code construction \cite{doi:10.1007/s11128-006-0047-9}.'
+    - code_id: quantum_ag
   cousins:
     - code_id: goppa
       detail: 'Classical Goppa codes over various algebraic curves are used to construct quantum Goppa codes.'
-    - code_id: quantum_triorthogonal
-      detail: 'By defining a generalization of triorthogonal matrices to Galois qudits of dimension \(q=2^m\), one can construct an asymptotically good family of quantum Goppa codes that admits a diagonal transversal gate at the third level of the \term{Clifford hierarchy} and attains a zero magic-state yield parameter, \(\gamma = 0\) \cite{arxiv:2408.07764}. This code can be treated as a qubit code by decomposing each Galois qudit into a Kronecker product of \(m\) qubits; see \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Two other such asymptotically good families exist \cite{arxiv:2408.09254,arxiv:2408.10140}, admitting a different diagonal gate at the third level of the \term{Clifford hierarchy}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/stabilizer/evaluation/quantum_ag.yml

@@ -0,0 +1,46 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: quantum_ag
+physical: galois
+logical: galois
+
+name: 'Quantum AG code'
+introduced: '\cite{arxiv:quant-ph/0107129}'
+
+description: |
+  A Galois-qudit CSS code constructed using two linear AG codes.
+  
+
+features:
+  rate: 'Quantum AG codes \cite{arxiv:quant-ph/0107129} can be asymptotically good. There exist three such families \cite{arxiv:2408.07764,arxiv:2408.09254,arxiv:2408.10140} that admit a diagonal transversal gate at the third level of the \term{Clifford hierarchy}.'
+
+  magic_scaling_exponent: 'By defining a generalization of triorthogonal matrices to Galois qudits of dimension \(q=2^m\), one can construct an asymptotically good family of quantum AG codes that admits a diagonal transversal gate at the third level of the \term{Clifford hierarchy} and attains a zero magic-state yield parameter, \(\gamma = 0\) \cite{arxiv:2408.07764}. This code can be treated as a qubit code by decomposing each Galois qudit into a Kronecker product of \(m\) qubits; see \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Two other such asymptotically good families exist \cite{arxiv:2408.09254,arxiv:2408.10140}, admitting a different diagonal gate at the third level of the \term{Clifford hierarchy}.'
+
+
+  encoders:
+    - 'Encoding defined in Ref. \cite{arxiv:quant-ph/0107129} uses a technique from Ref. \cite{arxiv:quant-ph/0005008} to encode quantum stabilizer codes.'
+
+  transversal_gates:
+    - 'There exist three asymptotically good code families \cite{arxiv:2408.07764,arxiv:2408.09254,arxiv:2408.10140} that admit a diagonal transversal gate at the third level of the \term{Clifford hierarchy}.'
+
+relations:
+  parents:
+    - code_id: galois_css
+      detail: 'Quantum AG codes can be realized in the CSS code construction \cite{doi:10.1007/s11128-006-0047-9}.'
+  cousins:
+    - code_id: ag
+    - code_id: quantum_triorthogonal
+      detail: 'By defining a generalization of triorthogonal matrices to Galois qudits of dimension \(q=2^m\), one can construct an asymptotically good family of quantum AG codes that admits a diagonal transversal gate at the third level of the \term{Clifford hierarchy} and attains a zero magic-state yield parameter, \(\gamma = 0\) \cite{arxiv:2408.07764}. This code can be treated as a qubit code by decomposing each Galois qudit into a Kronecker product of \(m\) qubits; see \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Two other such asymptotically good families exist \cite{arxiv:2408.09254,arxiv:2408.10140}, admitting a different diagonal gate at the third level of the \term{Clifford hierarchy}.'
+    - code_id: shimura
+      detail: 'The AG codes used in an asymptotically good construction of quantum AG codes with non-Clifford transversal gates \cite{arxiv:2408.09254} are those of the TVZ codes.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-08-23'

codes/quantum/qudits_galois/stabilizer/evaluation/rs/galois_grs.yml

@@ -25,8 +25,8 @@ relations:
     - code_id: generalized_reed_solomon
     - code_id: quantum_mds
       detail: 'Some Galois-qudit GRS codes are quantum MDS \cite{arxiv:1311.3009}.'
-    - code_id: galois_css
-      detail: 'Galois-qudit GRS codes can be constructed via the CSS construction or the Hermitian construction.'
+    - code_id: quantum_ag
+      detail: 'Galois-qudit GRS codes can be constructed via the CSS construction or the Hermitian construction from GRS codes, which are evaluation AG codes.'
     - code_id: stabilizer_over_gfqsq
       detail: 'Galois-qudit GRS codes can be constructed via the CSS construction or the Hermitian construction.'
     - code_id: quantum_concatenated