ref

codes/quantum/qubits/dynamic/floquet/da.yml

@@ -73,7 +73,7 @@ relations:
     - code_id: topological_abelian
       detail: 'Useful measurement sequences of DA codes can be extracted from topological quantum field theory \cite{arxiv:2307.10353}.'
     - code_id: translationally_invariant_stabilizer
-      detail: 'DA codes are typically defined on 2D and 3D lattices, but they are not conventional stabilizer codes in that they use code switching for error correction and gates.'
+      detail: 'DA codes are typically defined on 2D and 3D lattices, but they are not conventional stabilizer codes in that they use \hyperref[topic:code-switching]{code switching} for error correction and gates.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/small_distance/small/stab_10_1_2.yml

@@ -21,10 +21,10 @@ features:
     - 'Magic-state distillation protocol \cite{arxiv:2112.01446}.'
 
   fault_tolerance:
-    - '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}.'
+    - 'A fault-tolerant universal gate set can be done via \hyperref[topic:code-switching]{code switching} between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'
 
 realizations:
-  - 'Trapped-ion devices: fault-tolerant universal gate set via code switching between the Steane code and the \([[10,1,2]]\) code on a device from the Monz group \cite{arxiv:2403.13732}.'
+  - 'Trapped-ion devices: fault-tolerant universal gate set via \hyperref[topic:code-switching]{code switching} between the Steane code and the \([[10,1,2]]\) code on a device from the Monz group \cite{arxiv:2403.13732}.'
 
 relations:
   parents:
@@ -34,7 +34,7 @@ relations:
     - code_id: stab_15_1_3
       detail: 'The \([[10,1,2]]\) code can be obtained by morphing the \([[15,1,3]]\) code \cite{arxiv:2112.01446}.'
     - code_id: steane
-      detail: '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}.'
+      detail: 'A fault-tolerant universal gate set can be done via \hyperref[topic:code-switching]{code switching} between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'
 
 
 # Begin Entry Meta Information

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

@@ -71,8 +71,8 @@ features:
     - 'Shor error correction fidelity calculation \cite{arxiv:1101.1950,arxiv:1109.1714}.'
 
   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}.'
+    - 'A fault-tolerant universal gate set can be done via \hyperref[topic:code-switching]{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 \hyperref[topic:code-switching]{code switching} between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.'
     - '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}.'
     - 'Fault-tolerant logical zero and logical plus state preparation on all-to-all and 2D grid qubit connectivity \cite{arxiv:2402.17761}.'
@@ -86,7 +86,7 @@ realizations:
   Fault-tolerant universal two-qubit gate set using T injection by Monz group \cite{arxiv:2111.12654}.
   Logical CNOT gate and Bell-pair creation between two logical qubits (yielding a logical fidelity higher than physical), including rounds of correction and fault-tolerant primitives such as flag qubits and pieceable fault tolerance, on a 20-qubit device by Quantinuum \cite{arxiv:2208.01863}; logical fidelity interval of the combined preparation-CNOT-measurement procedure was higher than that of the unencoded physical qubits.
   Multiple rounds of Steane error correction \cite{arxiv:2312.09745}.
-  Fault-tolerant universal gate set via code switching between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.
+  Fault-tolerant universal gate set via \hyperref[topic:code-switching]{code switching} between the Steane code and the \([[10,1,2]]\) code \cite{arxiv:2403.13732}.
   Post-selected fault-tolerant logical Bell-state preparation with logical error rates at least 10 times lower than physical rate on a device by Quantinuum \cite{arxiv:2404.02280}.
   The quantum Fourier transform on three code blocks \cite{arxiv:2404.08616}.
   Fault-tolerant transversal and lattice-surgery state teleportation protocols as well as Knill error correction \cite{arxiv:2404.16728}.

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -156,6 +156,7 @@ features:
     - 'Syndrome extraction using flag qubits and classical codes \cite{arxiv:2212.10738}.'
     - 'Fault-tolerant constant-depth unencoder transforming logical states into physical states using single-qubit measurements \cite{arxiv:2408.06299}.'
     - 'Post-selection based algorithm preparing magic state corresponding to arbitrary rotations \cite{arxiv:2303.17380}.'
+    - '\hyperref[topic:code-switching]{Code switching} can be done using only transversal gates for qubit stabilizer codes \cite{arxiv:2409.13465}.'
 
   code_capacity_threshold:
     - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}. The AQEC relative entropy is related to the resulting threshold \cite{arxiv:2312.16991}.'

codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml

@@ -57,7 +57,7 @@ features:
 
   general_gates:
     - 'Magic-state distillation protocols \cite{doi:10.7907/059V-MG69}.'
-    - 'Non-clifford gates can be implemented via code switching \cite{doi:10.7907/059V-MG69}.'
+    - 'Non-clifford gates can be implemented via \hyperref[topic:code-switching]{code switching} \cite{doi:10.7907/059V-MG69}.'
 
   decoders:
     - 'Projection decoder of \(O(n^4)\) complexity \cite{arxiv:1308.6207}, modified to account for syndrome errors \cite{arxiv:1402.3037}.'

codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml

@@ -27,7 +27,7 @@ features:
 
   general_gates:
     - 'Magic-state distillation protocols \cite{doi:10.7907/059V-MG69}.'
-    - 'Non-clifford gates can be implemented via code switching \cite{doi:10.7907/059V-MG69}.'
+    - 'Non-clifford gates can be implemented via \hyperref[topic:code-switching]{code switching} \cite{doi:10.7907/059V-MG69}.'
 
   decoders:
     - 'Decoder that maps 3D color code to three copies of the 3D surface code \cite{arxiv:1606.00960}.'

codes/quantum/qubits/stabilizer/topological/color/3d_color/stab_15_1_3.yml

@@ -39,7 +39,7 @@ features:
     - 'Numerical study of \hyperref[topic:computational-threshold]{concatenated thresholds} of logical CNOT gates for various codes against depolarizing noise \cite{arxiv:0711.1556}.'
 
   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 \hyperref[topic:code-switching]{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}.'
     - 'Fault-tolerant logical zero and logical plus state preparation \cite{arxiv:2402.17761}.'
 
 
@@ -56,7 +56,7 @@ relations:
     - code_id: doubled_color
       detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}.'
     - code_id: steane
-      detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}. 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,arxiv:2306.17686}. An \([[105,1,3]]\) alternative concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are close to transversal \cite{arxiv:1309.3310,arxiv:1710.07256}.'
+      detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}. A fault-tolerant universal gate set can be done via \hyperref[topic:code-switching]{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,arxiv:2306.17686}. An \([[105,1,3]]\) alternative concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are close to transversal \cite{arxiv:1309.3310,arxiv:1710.07256}.'
     - code_id: concatenated_steane
       detail: 'The \([[105,1]]\) concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are transversal w.r.t. to two different partitions \cite{arxiv:1309.3310,arxiv:1710.07256}.'
     - code_id: qubit_concatenated

codes/quantum/qudits/stabilizer/qudit_stabilizer.yml

@@ -37,9 +37,10 @@ description: |
   \mathsf{S}\to\mathsf{N}_{\left\langle \mathsf{S},\mathsf{F}\right\rangle }\left(\mathsf{F}\right)~,
   \end{align}
   where \(\mathsf{Z}\) denotes taking the center of a group (e.g., see \cite{doi:10.1017/CBO9780511976667,arxiv:2402.00145} for proofs).
-  Code switching may not preserve the logical information and instead implement logical measurements; conditions on \(\mathsf{S}\) and \(\mathsf{F}\) such that qubit stabilizer code switching preserves logical information are derived in \cite[Prop. II.1]{arxiv:2304.01277}.
-  Clifford operations and Pauli measurements can be expressed as sequences of code switching \cite{arxiv:2401.12017}.
-  In the context of stabilizer codes realizing Abelian topological phases, code switching implements \textit{anyon condensation} of any anyons represented by operators in the group \(\mathsf{F}\).
+  Code switching may not preserve the logical information and instead implement logical measurements; conditions on \(\mathsf{S}\) and \(\mathsf{F}\) such that qubit stabilizer \hyperref[topic:code-switching]{code switching} preserves logical information are derived in \cite[Prop. II.1]{arxiv:2304.01277}.
+  Clifford operations and Pauli measurements can be expressed as sequences of \hyperref[topic:code-switching]{code switching} \cite{arxiv:2401.12017}.
+  In the context of stabilizer codes realizing Abelian topological phases, \hyperref[topic:code-switching]{code switching} implements \textit{anyon condensation} of any anyons represented by operators in the group \(\mathsf{F}\).
+  Code switching can be done using only transversal gates for qubit stabilizer codes \cite{arxiv:2409.13465}.
   \end{defterm}
 
   Modular-qudit stabilizer states can be expressed in terms of linear and quadratic functions over \(\mathbb{Z}_q^n\) \cite{arxiv:quant-ph/0408190}.