~

codes/quantum/qubits/stabilizer/css/goy.yml → codes/quantum/qubits/small_distance/goy.yml

@@ -7,11 +7,11 @@ code_id: goy
 physical: qubits
 logical: qubits
 
-name: '\([[6k,2k,2]]\) Ganti-Onunkwo-Young code'
+name: '\([[6r,2r,2]]\) Ganti-Onunkwo-Young code'
 introduced: '\cite{arXiv:1309.1674}'
 
 description: |
-  A member of the family of \([[6k,2k,2]]\) CSS codes designed to suppress errors in adiabatic quantum computation.
+  A member of the family of \([[6r,2r,2]]\) CSS codes designed to suppress errors in adiabatic quantum computation.
   All but two of its stabilizer generators are weight-two (two-body), and the remaining two are weight-\(4k\).
 
 features:

codes/quantum/qubits/small_distance/small/4/stab_4_2_2.yml

@@ -45,7 +45,7 @@ protection: |
   An equivalent version of this code can suppress errors in adiabatic quantum computation by being used as an excited-state space of a particular Hamiltonian \cite{arxiv:2412.07764}.
 
 features:
-  magic_scaling_exponent: 'Various magic-state distillation protocols exist for the \([[4,2,2]]\) qubit code and the \([[6,2,2]]\) \(C_6\) code in what are known as Meier-Eastin-Knill (MEK) protocols \cite{arxiv:1204.4221}.
+  magic_scaling_exponent: 'Various magic-state distillation protocols exist for the \([[4,2,2]]\) qubit code and the \(C_6\) code in what are known as Meier-Eastin-Knill (MEK) protocols \cite{arxiv:1204.4221}.
   For example, the magic-state yield parameter is \(\gamma = \log_2 5 \approx 2.322\) for a protocol using the \([[10,2,2]]\) code \cite[Box 2]{arxiv:1612.07330}; see also \cite[Table IV]{arxiv:1709.02789}.'
 
   transversal_gates:
@@ -59,8 +59,8 @@ features:
   fault_tolerance:
     - 'Preparation of certain states, both magic and non-magic, along with transversal gates can be performed fault-tolerantly, but requires post-selection because the code cannot correct errors \cite{arxiv:1610.03507}.
     Magic states can be injected into surface and color codes since the code is a small instance of both \cite{arxiv:2305.13581}.'
-    - 'Concatenations of \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).'
-    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
+    - 'Concatenations of \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).'
+    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
     - 'Fault-tolerant implementation of the Deutsch-Josza algorithm \cite{arxiv:2412.04791}.'
 
 
@@ -117,8 +117,8 @@ relations:
     - code_id: qubit_concatenated
       detail: |
         The \(\{|\overline{00}\rangle,|\overline{01}\rangle\}\) \([[4,1,2]]\) subcode is the smallest QPC, i.e., a concatenation of a two-qubit bit-flip with a two-qubit phase-flip repetition code.
-        Concatenations of \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).
-        Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
+        Concatenations of \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).
+        Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
         Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{arxiv:1604.04062}.
         The \([[4,2,2]]\) code can be concatenated with two copies of the surface code to yield the 4.6.12 color code \cite{arxiv:1604.04062}.
         An \([[8,1,2]]\) QPC correcting a single \hyperref[topic:ad]{AD} error is equivalent to a concatenation of the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) (constant-excitation) subcode of the \([[4,2,2]]\) code with the dual-rail code \cite{arxiv:quant-ph/0103042,arxiv:quant-ph/0501184,arxiv:2010.00538}. More generally, an \([[m^2,1,m]]\) QPC corrects \(m-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}.

codes/quantum/qubits/small_distance/small/6/stab_6_2_2.yml

@@ -15,25 +15,26 @@ description: |
   A set of stabilizer generators is \(IIXXXX\) and \(XXIIXX\), together with the same two \(Z\)-type generators.
 
 features:
-  magic_scaling_exponent: 'Various magic-state distillation protocols exist for the \([[4,2,2]]\) qubit code and the \([[6,2,2]]\) \(C_6\) code in what are known as Meier-Eastin-Knill (MEK) protocols \cite{arxiv:1204.4221}.
+  magic_scaling_exponent: 'Various magic-state distillation protocols exist for the \([[4,2,2]]\) qubit code and the \(C_6\) code in what are known as Meier-Eastin-Knill (MEK) protocols \cite{arxiv:1204.4221}.
   For example, the magic-state yield parameter is \(\gamma = \log_2 5 \approx 2.322\) for a protocol using the \([[10,2,2]]\) code \cite[Box 2]{arxiv:1612.07330}; see also \cite[Table IV]{arxiv:1709.02789}.'
 
   fault_tolerance:
-    - 'Concatenations of \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).'
-    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
+    - 'Concatenations of \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}).'
+    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
 
 relations:
   parents:
+    - code_id: goy
+      detail: 'The Ganti-Onunkwo-Young code for \(r=1\) is the \(C_6\) code.'
     - code_id: kls
-      detail: 'The Khesin-Lu-Shor code for \(r=2\) and \(m=2^r - 1 = 3\) is the \([[6,2,2]]\) \(C_6\) code.'
-    - code_id: small_distance_quantum
+      detail: 'The Khesin-Lu-Shor code for \(r=2\) and \(m=2^r - 1 = 3\) is the \(C_6\) code.'
   cousins:
     - code_id: qubit_concatenated
-      detail: 'Concatenations of \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}) and the Meier-Eastin-Knill (MEK) magic-state distillation protocols \cite{arxiv:1204.4221}.
-      Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
+      detail: 'Concatenations of \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}) and the Meier-Eastin-Knill (MEK) magic-state distillation protocols \cite{arxiv:1204.4221}.
+      Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
     - code_id: stab_4_2_2
-      detail: 'Concatenations of \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}) and the Meier-Eastin-Knill (MEK) magic-state distillation protocols \cite{arxiv:1204.4221}.
-      Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
+      detail: 'Concatenations of \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation schemes \cite{arxiv:quant-ph/0410199} (see also Ref. \cite{arxiv:quant-ph/0612073}) and the Meier-Eastin-Knill (MEK) magic-state distillation protocols \cite{arxiv:1204.4221}.
+      Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826,arxiv:2402.09606}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml

@@ -42,11 +42,11 @@ relations:
     - code_id: simplex
       detail: 'Quantum Hamming codes result from applying the CSS construction to Hamming codes and their duals the simplex codes.'
     - code_id: qubit_concatenated
-      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
+      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
     - code_id: stab_4_2_2
-      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
+      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
     - code_id: stab_6_2_2
-      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
+      detail: 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
     - code_id: surface
       detail: 'Quantum Hamming codes can be concatened with surface codes \cite{arxiv:2407.16176}.'
     - code_id: qubit_concatenated

codes/quantum/qubits/subsystem/qldpc/bbs/trapezoid.yml

@@ -27,7 +27,7 @@ relations:
     - code_id: iceberg
       detail: 'The trapezoid code family can be obtained from the \([[2m,2m-2,2]]\) error-detecting code by using some logical qubits as gauge qubits and imposing a two-dimensional qubit geometry \cite{arXiv:2412.06744}.'
     - code_id: goy
-      detail: 'The even-logical-qubit trapezoid family at \(l=k\) \cite{arxiv:1911.01354} is a subsystem version of the \([[6k,2k,2]]\) Ganti-Onunkwo-Young code. '
+      detail: 'The even-logical-qubit trapezoid family at \(l=k\) is a subsystem version of the Ganti-Onunkwo-Young code \cite{arxiv:1911.01354}.'
     - code_id: small_distance_quantum