Merge branch 'main' into correct-typo

codes/classical/properties/block/universally_optimal/t-designs.yml

@@ -8,6 +8,7 @@ code_id: t-designs
 name: '\(t\)-design'
 
 alternative_names:
+  - 'Quadrature'
   - 'Cubature'
   - 'Averaging set'
 
@@ -36,7 +37,7 @@ description: |
   Designs also exist on groups.
   Designs on the unitary (projective unitary) group are called strong unitary (unitary) designs \cite{arxiv:quant-ph/0512217,arxiv:quant-ph/0606161,arXiv:quant-ph/0611002}, while \(t\)-designs on the permutation group are called permutation \(t\)-designs \cite{doi:10.1017/S0963548300001917} (a.k.a. \(t\)-wise independent permutations).
 
-  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}, and designs on vertex operator algebras (a.k.a. conformal designs) \cite{arXiv:math/0701626}.
+  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}, quantum-channel designs \cite{arxiv:2412.09672}, and designs on vertex operator algebras (a.k.a. conformal designs) \cite{arXiv:math/0701626}.
   Existence has been proven for combinatorial designs \cite{arxiv:1401.3665,doi:10.1016/0012-365X(87)90061-6,arxiv:1611.06827,arxiv:1802.05900,arxiv:2411.18291}, subspace designs \cite{doi:10.1016/j.jcta.2014.06.001,arxiv:2212.00870}, as well as designs on continuous topological spaces \cite{doi:10.1016/0001-8708(84)90022-7,arxiv:1111.5900,arxiv:1112.4900}.
 
 #  when restricted to act on distinct \(t\)-tuples; see \cite[Remarks 6-7]{arXiv:2404.14648}

codes/quantum/qubits/small_distance/quantum_repetition.yml

@@ -55,7 +55,7 @@ realizations:
   - 'Trapped ions: 3-qubit bit-flip code by Wineland group \cite{doi:10.1038/nature03074}, and 3-qubit phase-flip algorithm implemented in 3 cycles on high fidelity gate operations \cite{doi:10.1126/science.1203329}.
   Both phase- and bit-flip codes for 31 qubits and their stabilizer measurements have been realized by Quantinuum \cite{arxiv:2305.03828}.
   Multiple rounds of Steane error correction \cite{arxiv:2312.09745}.'
-  - 'Superconducting circuits: 3-qubit phase-flip and bit-flip code by Schoelkopf group \cite{arxiv:1004.4324,arxiv:1109.4948}; 3-qubit bit-flip code \cite{arxiv:1411.5542}; 3-qubit phase-flip code up to 3 cycles of error correction \cite{arxiv:1508.01388}; IBM 15-qubit device \cite{arxiv:1709.00990}; IBM Rochester device using 43-qubit code \cite{arxiv:2004.11037}; Google system performing up to 8 error-correction cycles on 5 and 9 qubits \cite{arxiv:1411.7403}; Google Quantum AI Sycamore utilizing up to 11 physical qubits and running 50 correction rounds \cite{arxiv:2102.06132}; Google Quantum AI Sycamore utilizing up to 25 qubits for comparison of logical error scaling with a quantum code \cite{arxiv:2207.06431} (see also \cite{arxiv:2211.04728}). Google Quantum AI follow-up experiment on codes up to (classical) distance 29, demonstrating exponential suppression to an error floor of \(10^{-10}\) \cite{arxiv:2408.13687}. GHZ state on 75 qubits made on IBM device \cite{arxiv:2411.14638}.'
+  - 'Superconducting circuits: 3-qubit phase-flip and bit-flip code by Schoelkopf group \cite{arxiv:1004.4324,arxiv:1109.4948}; 3-qubit bit-flip code \cite{arxiv:1411.5542}; 3-qubit phase-flip code up to 3 cycles of error correction \cite{arxiv:1508.01388}; IBM 15-qubit device \cite{arxiv:1709.00990}; IBM Rochester device using 43-qubit code \cite{arxiv:2004.11037}; Google system performing up to 8 error-correction cycles on 5 and 9 qubits \cite{arxiv:1411.7403}; Google Quantum AI Sycamore utilizing up to 11 physical qubits and running 50 correction rounds \cite{arxiv:2102.06132}; Google Quantum AI Sycamore utilizing up to 25 qubits for comparison of logical error scaling with a quantum code \cite{arxiv:2207.06431} (see also \cite{arxiv:2211.04728}). Google Quantum AI follow-up experiment on codes up to (classical) distance 29, demonstrating exponential suppression to an error floor of \(10^{-10}\) \cite{arxiv:2408.13687}. Ising-model Nishimori phase transition realized for GHZ states on 54 qubits on a 127 qubit IBM device \cite{arxiv:2309.02863}. GHZ state on 75 qubits made on an IBM device \cite{arxiv:2411.14638}.'
   - 'Continuous error correction protocols have been implemented on a 3-qubit superconducting qubit device \cite{arxiv:2107.11398}.'
   - 'Semiconductor spin-qubit devices: 3-qubit devices at RIKEN \cite{arxiv:2201.08581} and Delft \cite{arxiv:2202.11530}.'
   - 'Nitrogen-vacancy centers in diamond: 3-qubit phase-flip code \cite{arxiv:1309.6424,doi:10.1038/s42005-022-00875-6} (see also Ref. \cite{arxiv:1309.5452}).'

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

@@ -31,7 +31,7 @@ description: |
     I & I & I & I & I & I & Z & Z & I \\
     I & I & I & I & I & I & I & Z & Z \\
     X & X & X & X & X & X & I & I & I \\
-    X & X & X & X & X & X & I & I & I
+    I & I & I & X & X & X & X & X & X
     \end{bmatrix}~.
   \end{align}
   The \hyperref[topic:encoder-respecting]{encoder-respecting form} of the Shor code is a star-shaped tree graph \cite{arxiv:2411.14448}.