Gottesman refs

codes/oaecc.yml

@@ -28,7 +28,7 @@ description: |-
   \begin{align}\mathcal{A} = \bigoplus_\gamma I_\gamma \otimes \mathcal{L}(\mathsf{B}_\gamma),\end{align}
   where \(\mathcal{L}(\mathsf{B}_\gamma)\) denotes the full set of linear maps on \(\mathsf{B}_\gamma\).
   The \(\mathsf{A}_j\) factors can be used to store quantum information, \(\gamma\) indexes the block structure of the code, while \(\mathsf{B}_j\) determine its gauge structure.
-  Together, the above forms the most general form of an information preserving structure \cite{arxiv:quant-ph/0507213,arxiv:0705.4282,arxiv:1006.1358}.
+  Together, the above forms the most general form of an information preserving structure \cite{arxiv:quant-ph/0402056,arxiv:quant-ph/0507213,arxiv:0705.4282,arxiv:1006.1358}.
 
 protection: |
   Given an error operation \(\mathcal{E}\), one says that \(\mathcal{A}\) is \textit{correctable} for \(\mathcal{E}\) if there exists a recovery operation \(\mathcal{R}\) such that

codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml

@@ -33,9 +33,6 @@ features:
   fault_tolerance:
     - 'Dual-rail qubits can be used to convert leakage and \hyperref[topic:ad]{AD} noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}.'
 
-  threshold:
-    - 'Between \(1.78\%\) and \(11.5\%\) with faulty photon detectors when repeatedly concatenating with the Steane code \cite{arxiv:quant-ph/0502101}.'
-
 realizations:
   - 'The dual-rail code is ubiquitous in linear-optical quantum devices and is behind the KLM protocol, one of the first proposals for fault-tolerant computation.
   See reviews \cite{arxiv:quant-ph/0512104,arxiv:quant-ph/0512071,arxiv:1907.06331} for more details.'
@@ -55,7 +52,9 @@ relations:
       detail: 'The two-mode binomial code for \(S=N=0\) reduces to the dual-rail code.'
   cousins:
     - code_id: oscillators_concatenated
-      detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code \cite{doi:10.1038/35051009}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
+      detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code such as the Steane code \cite{doi:10.1038/35051009,arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
+    - code_id: steane
+      detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code such as the Steane code \cite{doi:10.1038/35051009,arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}.' 
     - code_id: single-mode
       detail: 'Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.'
     - code_id: ampdamp

codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml

@@ -53,8 +53,9 @@ features:
     - 'Pieceable fault-tolerant CZ, CNOT, and CCZ gates \cite{arxiv:1603.03948}.'
   decoders:
     - 'Fault-tolerant syndrome extraction circuits \cite{arxiv:quant-ph/9605031,arxiv:quant-ph/9608028}.'
-    - 'Syndrome extraction circuit using only CNOT-SWAP gates \cite{arxiv:2207.13356}.'
+    - 'Syndrome extraction circuit optimized for a linear qubit architecture \cite{arxiv:quant-ph/0311116}.'
     - 'Combined dynamical decoupling and error correction protocol on individually-controlled qubits with always-on Ising couplings \cite{arxiv:1509.01239}.'
+    - 'Syndrome extraction circuit using only CNOT-SWAP gates \cite{arxiv:2207.13356}.'
     - 'Symmetric decoder correcting all weight-one Pauli errors. The resulting logical error channel after coherent noise has been explicitly derived \cite{arxiv:2203.01706}.'
     - 'Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2409.13681}.'
 

codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml

@@ -12,7 +12,7 @@ introduced: '\cite{arxiv:quant-ph/9608006}'
 
 alternative_names:
   - 'Calderbank-Rains-Shor-Sloane (CRSS) code'
-  - '\(GF(4)\)-linear code'
+  - '\(GF(4)\)-linear stabilizer code'
   - '\(M_{3}\) code'
 #   - 'Stabilizer code over \(GF(4)\)'
 # M3 <-- 1702.06990

codes/quantum/qubits/stabilizer/qldpc/concatenated/concatenated_steane.yml

@@ -27,6 +27,7 @@ features:
     code_capacity_threshold:
       - 'This family is one of the first to admit a \hyperref[topic:computational-threshold]{concatenated threshold} \cite{arxiv:quant-ph/9702058,arxiv:quant-ph/9809054,arxiv:quant-ph/0207119,arxiv:quant-ph/0410047,arxiv:quant-ph/0504218,arxiv:quant-ph/0703230,arxiv:quant-ph/0604090}; see the book \cite{preset:GottesmanBook}.'
     threshold:
+      - 'Between \(1.78\%\) and \(11.5\%\) with faulty photon detectors when combined with the dual-rail code at the first concatenation step in a variant of the KLM protocol \cite{arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}.'
       - 'Numerical study of \hyperref[topic:computational-threshold]{concatenated thresholds} of logical CNOT gates for various codes against depolarizing noise \cite{arxiv:0711.1556}; see also \cite{arxiv:quant-ph/0406025}.'
       - 'A \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
 

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -12,6 +12,7 @@ introduced: '\cite{arxiv:quant-ph/9605005,arxiv:quant-ph/9705052}'
 
 alternative_names:
   - 'Pauli stabilizer code'
+  - 'Symplectic code'
   - 'Additive quantum code'
   - 'Additive CWS code'
   - 'Clifford code'
@@ -81,7 +82,7 @@ description: |
   The sets of \(GF(4)\)-represented vectors for all generators yield a trace-Hermitian self-orthogonal additive quaternary code.
   This classical code corresponds to the stabilizer group \(\mathsf{S}\) while its trace-Hermitian dual corresponds to the normalizer \(\mathsf{N(S)}\).
   In the case of stabilizer states, the correspondence is between such states and trace-Hermitian self-dual quaternary codes; such codes, and therefore such states, have been classified up to equivalence for \(n \leq 12\) \cite{arxiv:quant-ph/0503236,arxiv:math/0504522}.
-  There is a complete set of invariants characterizing stabilizer states up to equivalence \cite{arxiv:quant-ph/0410165}.
+  There is a complete set of invariants characterizing stabilizer states up to equivalence \cite{arxiv:quant-ph/0410165,arxiv:quant-ph/0404106}.
 
   ZX calculus is complete, sound, and universal for qubit stabilizer codes \cite{arxiv:1307.7025}.
   Any stabilizer code can be represented by a \textit{ZX canonical form} (ZXCF) \cite{arxiv:2411.14448}, and there exist two other representations \cite{arxiv:2205.02009,arxiv:2411.14448} that utilize ZX calculus.
@@ -173,6 +174,7 @@ features:
     - 'Greedy syndrome measurement schedule \cite{arxiv:2409.14283}.'
     - 'Dynamical weight reduction (DWR) scheme in which measurements of smaller-weight Paulis yield the outcome of a larger-weight Pauli via the use of ZX calculus and ancillary qubits \cite{arxiv:2410.12527}.'
     - 'Ancilla modes can be used for syndrome extraction instead of ancilla qubits \cite{arxiv:quant-ph/0511098}, and using two-component cat codes \cite{arxiv:1807.09334} yields fault-tolerant syndrome extraction circuits.'
+    - 'Continuous-time QEC protocol \cite{arxiv:quant-ph/0402017}.'
     - 'MPE decoding, i.e., the process of finding the most likely error, is \(NP\)-complete in general \cite{arxiv:1009.1319,manual:{Kuo, Kao-Yueh, and Chung-Chin Lu. "On the hardness of decoding quantum stabilizer codes under the depolarizing channel." 2012 International Symposium on Information Theory and its Applications. IEEE, 2012.}}. If the noise model is such that the most likely error is the lowest-weight error, then ML decoding is called \textit{minimum-weight} decoding. Maximum-likelihood (ML) decoding (a.k.a.\ degenerate maximum-likelihood decoding), i.e., the process of finding the most likely error class (up to degeneracy of errors), is \(\#P\)-complete in general \cite{arxiv:1310.3235}.'
     - 'Incorporating faulty syndrome measurements can be done by performing spacetime decoding, i.e., using data from past rounds for decoding syndromes in any given round. If a decoder does not process syndrome data sufficiently quickly, it can lead to the \textit{backlog problem} \cite{arxiv:1302.3428}, slowing down the computation.'
     - 'Splitting decoders \cite{arxiv:2309.15354}.'
@@ -219,7 +221,7 @@ notes:
   - 'Introductions to stabilizer codes can be found in \cite{arxiv:quant-ph/9705052,preset:PreskillNotes,doi:10.1002/9783527618637.ch1}.'
   - 'Tables of bounds and examples of stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Ref. \cite{doi:10.1007/978-3-540-37634-7_13}, are maintained by M. Grassl at this \href{https://codetables.markus-grassl.de/}{website}. A Magma implementation exists at this \href{https://magma.maths.usyd.edu.au/magma/handbook/text/1976}{website}.'
   - 'See Quantum Codes qubit stabilizer database, maintained by N. Aydin, P. Liu, and B. Yoshino \cite{arxiv:2106.12065,arxiv:2108.03567}, at this \href{https://quantumcodes.info/}{website}.'
-  - 'Entanglement purification protocols with qubit stabilizer codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0209091}. There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}.'
+  - 'Entanglement purification protocols with qubit stabilizer codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0209091}. There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}. Purification protocols using two-way classical channels can exceed the quantum Hamming and quantum Singleton bounds \cite{arxiv:quant-ph/0310097}.'
   - 'The overlap between any stabilizer codeword and any \(n\)-qubit product state is at most \(2/2^d\) \cite[Thm. 2]{arxiv:2405.01332}.'
   - 'Qubit stabilizer codes can be used to estimate physical Pauli noise up to their \hyperref[topic:quantum-weight-enumerator]{pure distance} \cite{arxiv:2107.14252}, and logical Pauli noise for any correctable physical noise \cite{arxiv:2209.09267}.'
   - 'The stabilizer formalism has been gamified \cite{arxiv:2405.06795}.'

codes/quantum/qudits/stabilizer/qudit_css.yml

@@ -8,7 +8,7 @@ physical: qudits
 logical: qudits
 
 name: 'Modular-qudit CSS code'
-introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029}'
+introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9703048}'
 
 description: |
   An \(((n,K,d))_q\) modular-qudit stabilizer code admitting a set of stabilizer generators that

codes/quantum/qudits_galois/stabilizer/css/galois_css.yml

@@ -8,7 +8,7 @@ physical: galois
 logical: galois
 
 name: 'Galois-qudit CSS code'
-introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9608049,arxiv:quant-ph/9703048,arxiv:quant-ph/9911011,arxiv:quant-ph/0312164,doi:10.1016/j.disc.2007.08.038}'
+introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9608049,arxiv:quant-ph/9911011,arxiv:quant-ph/0312164,doi:10.1016/j.disc.2007.08.038}'
 
 alternative_names:
   - 'Euclidean code'

codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml

@@ -11,7 +11,7 @@ name: 'Hermitian Galois-qudit code'
 introduced: '\cite[Corr. 5]{arxiv:quant-ph/9703048}\cite{doi:10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T,doi:10.1109/18.959288,arxiv:quant-ph/0508070}'
 
 alternative_names:
-    - '\(GF(q^2)\)-linear code'
+    - '\(GF(q^2)\)-linear stabilizer code'
 #   - 'Stabilizer code over \(GF(q^2)\)'
 
 description: |