Gottesman refs

codes/quantum/properties/qecc.yml

@@ -60,7 +60,7 @@ features:
 
 
 notes:
-  - 'See Refs. \cite{arxiv:quant-ph/9712048,doi:10.1090/gsm/047,doi:10.1017/CBO9780511976667,arxiv:quant-ph/0612185,arxiv:0904.2557,arxiv:0905.2794,arxiv:1302.3428,doi:10.1103/RevModPhys.88.041001,doi:10.1002/9783527805785.ch1,arxiv:1907.11157,preset:PreskillNotes,arxiv:1910.03672,doi:10.1002/9781119790327.ch10,arxiv:2407.12737} for overviews of quantum error correction.'
+  - 'See Refs. \cite{arxiv:quant-ph/9712048,doi:10.1090/gsm/047,doi:10.1017/CBO9780511976667,arxiv:quant-ph/0507174,arxiv:quant-ph/0612185,arxiv:0904.2557,arxiv:0905.2794,arxiv:1302.3428,doi:10.1103/RevModPhys.88.041001,doi:10.1002/9783527805785.ch1,arxiv:1907.11157,preset:PreskillNotes,arxiv:1910.03672,doi:10.1002/9781119790327.ch10,arxiv:2407.12737} for overviews of quantum error correction.'
   - 'See Refs. \cite{doi:10.1017/CBO9781139034807,doi:10.1201/b15868,preset:GottesmanBook} for books on quantum error correction.'
   - 'See video tutorials by \href{https://www.youtube.com/watch?v=_ls3KczZL2c}{V. V. Albert}, \href{https://www.youtube.com/watch?v=uD69GCYF9Zg}{S. M. Girvin}, \href{https://www.youtube.com/watch?v=buIbd_aXAHw}{P. Shor}, \href{https://www.youtube.com/watch?v=Je7sVJGKMgU}{B. Terhal}, and \href{https://www.youtube.com/watch?v=mcwpe8iJ5uo}{J. Wright}.'
   - 'Quantum error correction was initially claimed not to be theoretically possible \cite{arxiv:hep-th/9406058,doi:10.1098/rsta.1995.0106}.'

codes/quantum/qubits/nonstabilizer/jump.yml

@@ -21,6 +21,9 @@ protection: |
 features:
   rate: 'An infinite family of jump codes asymptotically attains an upper bound on \(K\) \cite[Thm. 27]{doi:10.1023/A:1024188005329}.'
 
+  general_gates:
+    - 'Two-qubit entangling gate \cite{arxiv:quant-ph/0506037}.'
+
 notes:
   - 'Survey of jump codes \cite{manual:{Jimbo, Masakazu, and Keisuke Shiromoto. "Quantum jump codes and related combinatorial designs." Information Security, Coding Theory and Related Combinatorics. IOS Press, 2011. 285-311.}}.'
 

codes/quantum/qubits/small_distance/quantum_repetition.yml

@@ -23,6 +23,7 @@ description: |
     \end{split}
   \end{align}
   showing that the phase-flip code stores information in the total parity of the qubits.
+  For example, an early code realized in devices is the 2-qubit phase-flip code, which encodes a logical qubit into Bell states \(|00\rangle+|11\rangle\) and \(|01\rangle+|10\rangle\).
 
 protection: |
   Bit-flip code detects bit-flip errors \(X\) on \(\left\lfloor (n-1)/2\right\rfloor\) qubits and does not detect any phase-flip errors \(Z\).
@@ -53,6 +54,7 @@ features:
 
 realizations:
   - 'NMR: 2-qubit phase-flip code \cite{arxiv:quant-ph/9811068}; 3-qubit phase-flip code \cite{arxiv:quant-ph/9802018,arxiv:1108.4842}, with up to two rounds of error correction in liquid-state NMR \cite{arxiv:1109.4821}. Such codes were used to characterize noise \cite{arxiv:quant-ph/0610038}.'
+  - 'Linear optics: 2-qubit phase-flip code \cite{arxiv:quant-ph/0502042}.'
   - '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}.'

codes/quantum/qubits/small_distance/small/7/steane/steane.yml

@@ -64,6 +64,7 @@ features:
     - 'The \hyperref[topic:clifford]{single-qubit Clifford group} \cite{arxiv:quant-ph/9605011,arxiv:0706.1382}.'
 
   general_gates:
+    - 'Fault-tolerant approximations of arbitrary single-qubit gates \cite{arxiv:quant-ph/0411206,arxiv:quant-ph/0506126}.'
     - '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}.'
     - 'Pieceable fault-tolerant CCZ gate \cite{arxiv:1603.03948}.'
 

codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml

@@ -64,6 +64,7 @@ features:
     The threshold under ML decoding corresponds to the value of a critical point of the 3D random-plaquette \(\mathbb{Z}_2\) gauge theory (3D-RPGM) via the statistical mechanical mapping \cite{arxiv:quant-ph/0110143}, calculated to be \(3.3 \%\) \cite{arxiv:quant-ph/0401101} (see also \cite{arxiv:cond-mat/0501372}).'
 
   fault_tolerance:
+    - 'There is a simple proof of a threshold for MBQC \cite{arxiv:quant-ph/0503130}.'
     - 'Photonic architecture \cite{arxiv:0808.1782}.'
     - 'Generalized foliation procedures exist for noise-bias preserving MBQC \cite{arxiv:2201.10566}.'
     - 'Fault complexes yield fault-tolerance properties of cluster states that come from foliations of codes \cite{arxiv:2410.12963}.'