refs

codes/quantum/properties/qecc.yml

@@ -63,7 +63,7 @@ notes:
   - '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}.'
-  - 'Resource-theoretic interpretations of quantum error correction have been developed, including those that think of codes together with recovery operations as superchannels (a.k.a. quantum combs or bipartite operations) \cite{arxiv:1210.4722,arxiv:1406.7142,arxiv:2405.17567,arxiv:2409.09416}.'
+  - 'Resource-theoretic interpretations of quantum error correction have been developed, including those that think of codes together with recovery operations as superchannels (a.k.a. quantum combs or bipartite operations) \cite{arxiv:1105.4464,arxiv:1210.4722,arxiv:1406.7142,arxiv:2405.17567,arxiv:2409.09416}.'
 
 
 # 20240704 subsystem QECC, hybrid QECC, and QECC are three children of OAQECC

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

@@ -70,6 +70,7 @@ realizations:
   - 'The CZ magic state has been realized on an IBM heavy-hex superconducting circuit device \cite{arxiv:2305.13581}.'
   - 'Logical Clifford gates for a twist-defect surface code that is single-qubit Clifford equivalent to a \([[4,1,2]]\) realized in a trapped ion device by Quantinuum \cite{arxiv:2406.09951}.'
   - 'CPC gadgets for the \([[4,2,2]]\) code have been implemented on the IBM 5Q superconducting device \cite{arxiv:1709.01866}.'
+  - 'An FPGA implementation of the collision clustering decoder \cite{arxiv:2309.05558} realized on a Rigetti supercondutcing device \cite{arxiv:2410.05202}.'
 
 
 relations:

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -134,14 +134,12 @@ features:
     - 'Generalized lattice surgery \cite{arxiv:2301.13738}.'
   fault_tolerance:
     - 'Steane error correction \cite{arxiv:quant-ph/9611027}, where fault-tolerance is ensured by preparing ancillary encoded states and extracting syndromes via \(CNOT\) gates.'
-    - 'Fault-tolerant error correction and logical measurements using flag qubits for distance-three cyclic CSS codes \cite{arxiv:1803.09758}.
-    Parallel syndrome extraction for distance-three codes can be done fault-tolerantly using one flag qubit \cite{arxiv:2208.00581}.
-    \hyperref[topic:effective-distance]{Distance-preserving} flag fault-tolerant error correction can be done using lookup tables for small codes \cite{arxiv:2306.12862}.
-    Any self-dual CSS code with bounded-weight stabilizer generators admits flag fault-tolerant syndrome extraction \cite{arxiv:1708.02246}.'
+    - 'Fault-tolerant error correction and logical measurements using flag qubits for distance-three cyclic CSS codes \cite{arxiv:1803.09758}. Parallel syndrome extraction for distance-three codes can be done fault-tolerantly using one flag qubit \cite{arxiv:2208.00581}. \hyperref[topic:effective-distance]{Distance-preserving} flag fault-tolerant error correction can be done using lookup tables for small codes \cite{arxiv:2306.12862}. Any self-dual CSS code with bounded-weight stabilizer generators admits flag fault-tolerant syndrome extraction \cite{arxiv:1708.02246}.'
     - 'Homomorphic gadgets fault-tolerant measurement unify Steane and Shor error correction \cite{arxiv:2211.03625}.'
     - 'A fault-tolerant error-correction protocol using \(O(d\log d)\) syndrome measurements can be applied to any CSS code with distance \(d \geq \Omega(n^{\alpha})\) for any \(\alpha > 0\) \cite{arxiv:2002.05180}.'
     - 'Fault-tolerant measurement-free scheme for low-distance CSS codes \cite{arxiv:2307.13296}.'
     - 'Automated fault-tolerant encoding circuit synthesis \cite{arxiv:2408.11894}.'
+    - 'Fault-tolerant homological measurement of logical Pauli operators \cite{arxiv:2410.02753}.'
   code_capacity_threshold:
     - 'Bounds on code capacity thresholds for various noise models exist in terms of stabilizer generator weights \cite{arxiv:1208.2317,arxiv:1412.6172}.'
   decoders:

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -165,6 +165,7 @@ features:
     - '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}.'
     - 'Flag-Proxy Networks (FPNs) \cite{arxiv:2409.14283}.'
+    - 'A logical Pauli can be \hyperref[topic:gauging-out]{gauged out} to yield a fault-tolerant measurement that requires a qubit overhead linear in the Pauli''s support \cite{arxiv:2410.02213}.'
 
   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}.'