refs

codes/quantum/oecc.yml

@@ -27,6 +27,7 @@ protection: |
   \Pi E^{\dagger}_a E_b \Pi = I_{\mathsf{A}} \otimes g_{ab}^{\mathsf{B}}
   \end{align}
   where \(\Pi\) is a projector onto the codespace \(\mathsf{C}\), and \(g_{ab}^{\mathsf{B}}\) is an arbitrary operator on the gauge subsystem.
+  These have also been studied in the presence of continuous noise \cite{arxiv:0806.3145}.
 
 features:
   encoders:

codes/quantum/properties/block/tensor_network/single_tensor/ame.yml

@@ -17,7 +17,7 @@ description: |
 
   \begin{defterm}{Absolutely maximally entangled (AME) state}
   \label{topic:ame}
-  A state on \(n\) subsystems is \(d\)\textit{-uniform} \cite{arXiv:quant-ph/0310137,arxiv:1404.3586} (a.k.a. \(d\)-maximally mixed \cite{arxiv:1211.4118}) if all reduced density matrices on up to \(d\) subsystems are maximally mixed.
+  A state on \(n\) subsystems is \(d\)\textit{-uniform} \cite{arXiv:quant-ph/0310137,arxiv:1404.3586} (a.k.a. \(d\)-undetermined \cite{arxiv:0809.3081} or \(d\)-maximally mixed \cite{arxiv:1211.4118}) if all reduced density matrices on up to \(d\) subsystems are maximally mixed.
   A \(K\)-dimensional subspace of \(d-1\)-uniform states of \(q\)-dimensional subsystems is equivalent to a \hyperref[topic:quantum-weight-enumerator]{pure} \(((n,K,d))_q\) code \cite{arxiv:0704.0251,arxiv:1907.07733}.
   An AME state (a.k.a. maximally multi-partite entangled state \cite{arxiv:0710.2868,arxiv:1002.2592}) is a \(\lfloor n/2 \rfloor\)-uniform state, corresponding to a \hyperref[topic:quantum-weight-enumerator]{pure} \(((n,1,\lfloor n/2 \rfloor + 1))_{\mathbb{Z}_q}\) code.
   The rank-\(n\) tensor formed by the encoding isometry of such codes is a \textit{perfect tensor} (a.k.a. multi-unitary tensor), meaning that it is proportional to an isometry for any bipartition of its indices into a set \(A\) and a complementary set \(A^{\perp}\) such that \(|A|\leq|A^{\perp}|\).

codes/quantum/qubits/stabilizer/convolutional/quantum_convolutional.yml

@@ -40,7 +40,7 @@ relations:
       detail: 'Quantum convolutional encoding circuits can be viewed as matrix-product-state tensor networks \cite{arxiv:1312.4578}.'
   cousins:
     - code_id: eaqecc
-      detail: 'Quantum convolutional codes have been extended to the EA setting \cite{arxiv:0712.2223,arxiv:0806.4214}.'
+      detail: 'Quantum convolutional codes have been extended to the EA setting \cite{arxiv:0712.2223,arxiv:0806.4214,arxiv:0807.3803}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/qubit_css.yml

@@ -157,6 +157,7 @@ notes:
   - 'See Refs. \cite{arxiv:quant-ph/9605021,doi:10.1017/CBO9780511976667,preset:PreskillNotes,preset:GottesmanBook} for simple examples of CSS codes.'
   - 'Introduction to \ref{topic:CSS-to-homology-correspondence} by \href{https://www.youtube.com/watch?v=SeLpWg_8qlc}{M. Hastings}; see also the book \cite{arxiv:1504.01444}.'
   - 'Entanglement purification protocols with qubit CSS codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0003004}.'
+  - 'Qubit CSS codes can be used in quantum repeaters \cite{arxiv:0809.3629}.'
 
 #  - 'Original requirement of \(C_X^\perp \subset C_Z\) \cite{arxiv:quant-ph/9512032} has been relaxed to absorb \hyperref[code:hypergraph_product]{hypergraph product} codes.'
 

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -129,7 +129,7 @@ features:
     - 'With pieceable fault-tolerance, any \hyperref[topic:degeneracy]{non-degenerate} stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of non-transversal fault-tolerant gates \cite{arxiv:1603.03948}.'
     - 'Shor error correction \cite{arxiv:quant-ph/9605011,arxiv:quant-ph/9605031}, in which fault tolerance against syndrome extraction errors is ensured by simply repeating syndrome measurements. A modification uses adaptive measurements \cite{arxiv:2208.05601}.'
     - 'Generalization of Steane error correction stabilizer codes \cite[Sec. 3.6]{manual:{Yoder, Theodore., \emph{DSpace@MIT} Practical Fault-Tolerant Quantum Computation (2018)}}.'
-    - 'Fault-tolerant error correction scheme by Knill (a.k.a. telecorrection \cite{arxiv:quant-ph/0601066}), which is based on teleportation \cite{arxiv:quant-ph/0410199,arxiv:quant-ph/0312190}.'
+    - 'Fault-tolerant error correction scheme by Knill (a.k.a. telecorrection \cite{arxiv:quant-ph/0601066}), which is based on teleportation \cite{arxiv:quant-ph/0410199,arxiv:quant-ph/0312190}. A variant of it has been termed the Fibonacci scheme \cite{arxiv:0809.5063}.'
     - 'Fault-tolerant error correction using flag qubits for codes satisfying certain conditions \cite{arxiv:1708.02246}.'
     - 'GHz state distillation for Steane error correction \cite{arxiv:2109.06248}.'
     - 'Syndrome extraction using flag qubits and classical codes \cite{arxiv:2212.10738}.'

codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml

@@ -77,6 +77,7 @@ features:
     - 'Numerical study of concatenated thresholds of logical CNOT gates for various codes against depolarizing noise \cite{arxiv:0711.1556}.'
     - 'The Bacon-Shor code has a \hyperref[topic:measurement-threshold]{measurement threshold} of zero \cite{arxiv:2402.00145}.'
   decoders:
+    - 'Message passing for \([[9,1,3,3]]\) Bacon-Shor code \cite{arxiv:0806.2188}.'
     - 'Both Steane error correction and Shor error correction can be used for syndrome extraction, with the former outperforming the latter \cite{arxiv:2403.01659}.'
     - 'Utilizing the mapping of the effect of the noise to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:2002.11733} yields several copies of the 1D Ising model \cite[Sec. V.B]{arxiv:0908.4246}.'
     - 'While check operators are few-body, stabilizer weights scale with the number of qubits, and stabilizer expectation values are obtained by taking products of gauge-operator expectation values.

codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_cws.yml

@@ -8,7 +8,7 @@ physical: qudits
 logical: qudits
 
 name: 'Modular-qudit CWS code'
-introduced: '\cite{arxiv:0712.1979,arxiv:0801.0831}'
+introduced: '\cite{arxiv:0712.1979,arxiv:0801.0831,arxiv:0808.3086}'
 
 description: |
   A CWS code for modular qudits, defined using a modular-qudit cluster state and a set of modular-qudit \(Z\)-type Pauli strings defined by a \(q\)-ary classical code over \(\mathbb{Z}_q\).