refs

codes/quantum/oscillators/oscillators.yml

@@ -24,6 +24,9 @@ description: |
   Alternatively, states can be represented as functions over the reals by expanding in a continuous "basis" (more technically, set of tempered distributions in the space dual to Schwartz space), such as the position "basis" \(|y\rangle\) with \(y\in\mathbb{R}\) or the momentum "basis" \(|p\rangle\) with \(p\in\mathbb{R}\).
   States can further be represented as functions over the joint position-momentum phase space in the Wigner function formalism \cite{doi:10.1103/PhysRev.40.749,doi:10.1103/PhysRevA.15.449}.
 
+  An important subset of states is formed by the \textit{Gaussian states}, which are in one-to-one correspondence with a (displacement) vector and covariance matrix \cite{arxiv:quant-ph/0410100,arxiv:0801.4604,arxiv:1110.3234,arxiv:2010.15518,arxiv:2409.11628}.
+  Pure Gaussian states can be obtained from the \textit{vacuum Fock state} \(|n=0\rangle\) via a Gaussian unitary transformation (defined below). 
+
 protection: |
   \subsection{Displacement error basis}
 

codes/quantum/properties/qecc.yml

@@ -63,7 +63,8 @@ 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}.'
-  - 'A resource theory of quantum error correction has been developed \cite{doi:10.1103/PhysRevA.110.032413}.'
+  - '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}.'
+
 
 # 20240704 subsystem QECC, hybrid QECC, and QECC are three children of OAQECC
 relations:

codes/quantum/qubits/majorana/fermions.yml

@@ -14,10 +14,11 @@ description: |
   Finite-dimensional quantum error-correcting code encoding a logical (qudit or fermionic) Hilbert space into a physical Fock space of fermionic modes.
   Codes are typically described using Majorana operators, which are linear combinations of fermionic creation and annihilation operators \cite{arxiv:quant-ph/0003137}.
 
+  Admissible codewords are called fermionic states, a subset of which is the Gaussian fermionic states \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}.
 
 features:
   general_gates:
-    - 'Clifford operations on fermionic codes can often be formulated using \textit{Fermionic Linear Optics}, a classically simulable model of computation \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.'
+    - 'Clifford operations on fermionic codes can often be formulated using \textit{Fermionic Linear Optics}, a classically simulable model of computation \cite{arxiv:quant-ph/0108033,arxiv:quant-ph/0108010,arxiv:quant-ph/0404180,arxiv:2010.15518,arxiv:2409.11628}. The structure of the Majorana Clifford group has been studied \cite{arxiv:2407.11319}.'
 
 notes:
   - 'See Ref. \cite{arxiv:1404.0897} for an introduction into Majorana-based qubits.'

codes/quantum/qubits/permutation_invariant/icosahedral_permutation_invariant.yml

@@ -10,6 +10,10 @@ logical: qubits
 name: '\(((7,2,3))\) Pollatsek-Ruskai code'
 introduced: '\cite{arxiv:quant-ph/0304153,arxiv:2005.10910,arxiv:2305.07023}'
 
+alternative_names:
+  - '\(((7,2,3))\) icosahedral code'
+
+
 description: |
   Seven-qubit PI code that realizes gates from the binary icosahedral group transversally.
   Can also be interpreted as a spin-\(7/2\) single-spin code.

codes/quantum/qubits/qubits_into_qubits.yml

@@ -122,6 +122,7 @@ features:
       where \(P\) is any Pauli matrix, where \(C_1\) is the \hyperref[topic:pauli]{Pauli group}, and where \(C_2\) is the \hyperref[topic:clifford]{Clifford group}.
       \end{defterm}'
     - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.'
+    - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.'
   decoders:
     - 'Incorporating faulty syndrome measurements can be done using the \textit{phenomenological noise model}, which simulates errors during syndrome extraction by flipping some of the bits of the measured syndrome bitstring. In the more involved \textit{circuit-level noise model}, every component of the syndrome extraction circuit can be faulty.'
     - 'The decoder determining the most likely error given a noise channel is called the \textit{maximum probability error} (MPE) decoder. For few-qubit codes (\(n\) is small), MPE decoding can be based by creating a lookup table. For infinite code families, the size of such a table scales exponentially with \(n\), so approximate decoding algorithms scaling polynomially with \(n\) have to be used.'
@@ -132,6 +133,7 @@ features:
   fault_tolerance:
     - 'There are lower bounds on the overhead of fault-tolerant QEC in terms of the capacity of the noise channel \cite{arxiv:2202.00119}. A more stringent bound applies to geometrically local QEC due to the fact that locality constrains the growth of the entanglement that is needed for protection \cite{arxiv:2302.04317}.'
     - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.'
+    - 'Fault-tolerant gates can be done for any code supporting a transversal implementation of Pauli gates using generalized gate teleportation \cite{arxiv:2409.11616}.'
   threshold:
     - '\begin{defterm}{Computational threshold}
       \label{topic:computational-threshold}

codes/quantum/qubits/stabilizer/topological/color/2d_color/triangular_color/triangular_color.yml

@@ -40,7 +40,7 @@ features:
 
   general_gates:
     - 'Lattice surgery scheme for a hybrid 6.6.6-4.8.8 layout yields lower resource overhead when compared to analogous surface code scheme \cite{arxiv:2201.07806}.'
-    - 'Low-overhead magic-state distillation circuit using flag qubits \cite{arxiv:2003.03049}.'
+    - 'Low-overhead magic-state distillation circuit using flag qubits \cite{arxiv:2003.03049} or lattice surgery \cite{arxiv:2409.07707}.'
 
   decoders:
     - 'Distance-three measurement schedule based on detector error models \cite{arxiv:2407.13826}.'