refs

codes/classical/properties/block/distributed_storage/lrc/lcc.yml

@@ -42,6 +42,8 @@ relations:
       detail: 'There are relations between LDCs and LTCs \cite{doi:10.1007/978-3-642-15369-3_50}.'
     - code_id: quantum_locally_recoverable
       detail: 'There is not a natural quantum version of LCCs \cite[Thm. 9]{arxiv:2311.08653}.'
+    - code_id: analog
+      detail: 'LCCs can also be defined over the real or complex numbers, and there are no complex 2-query LCCs \cite{arxiv:1009.4375}.'
 
 
 # Begin Entry Meta Information

codes/quantum/groups/topological/quantum_double.yml

@@ -17,7 +17,7 @@ description: |
   The physical Hilbert space has dimension \( |G|^E  \), where \( E \) is the number of  edges in the tessellation. The dimension of the code space is the number of orbits of the conjugation action of \( G \) on \( \text{Hom}(\pi_1(\Sigma),G) \), the set of group homomorphisms from the fundamental group of the surface \( \Sigma \) into the finite group \( G \) \cite{arxiv:1908.02829}. When \( G \) is Abelian, the formula for the dimension simplifies to \( |G|^{2g} \), where \( g \) is the genus of the surface \( \Sigma \).
 
   The codespace is the ground-state subspace of the quantum double model Hamiltonian, while local excitations are characterized by anyons.
-  Different types of anyons are labeled by irreducible representations of the group's quantum double algebra, \(D(G)\) (a.k.a. Drinfield center) \cite{arxiv:1006.5479}.
+  Different types of anyons are labeled by irreducible representations of the group's quantum double algebra, \(D(G)\) (a.k.a. Drinfield center) \cite{arxiv:1006.5479,arxiv:2310.19661}.
   Not all isomorphic non-Abelian groups give rise to different quantum doubles \cite{arxiv:math/0605530}.
 
   For non-Abelian groups, alternative constructions are possible, encoding information in the fusion space of the low-energy anyonic quasiparticle excitations of the model \cite{doi:10.1007/3-540-49208-9_31,arxiv:quant-ph/0306063,doi:10.1017/CBO9780511792908}.

codes/quantum/oscillators/fock_state/rotation/chebyshev.yml

@@ -9,7 +9,9 @@ name: 'Chebyshev code'
 introduced: '\cite{arxiv:1811.01450}'
 
 description: |
-  Single-mode bosonic Fock-state code that can be used for error-corrected sensing of a signal Hamiltonian \({\hat n}^s\), where \({\hat n}\) is the occupation number operator. Codewords for the \(s\)th-order Chebyshev code are
+  Single-mode bosonic Fock-state code that can be used for error-corrected sensing of a signal Hamiltonian \({\hat n}^s\), where \({\hat n}\) is the occupation number operator. 
+  
+  Codewords for the \(s\)th-order Chebyshev code are
   \begin{align}
   \begin{split}
   \ket{\overline 0} &=\sum_{k \text{~even}}^{[0,s]} \tilde{c}_k \Ket{\left\lfloor M\sin^2\left( k\pi/{2s}\right) \right\rfloor},\\

codes/quantum/oscillators/fock_state/rotation/number_phase.yml

@@ -15,7 +15,9 @@ alternative_names:
 # Ouyang
 
 description: |
-  Bosonic rotation code consisting of superpositions of Pegg-Barnett phase states \cite{doi:10.1088/0305-4470/19/18/030},
+  Bosonic rotation code consisting of superpositions of Pegg-Barnett phase states \cite{doi:10.1088/0305-4470/19/18/030}.
+
+  Pegg-Barnett phase states are expressed in terms of Fock states as
   \begin{align}
   |\phi\rangle \equiv \frac{1}{\sqrt{2\pi}}\sum_{n=0}^{\infty} \mathrm{e}^{\mathrm{i} n \phi} \ket{n}.
   \end{align}

codes/quantum/properties/asymmetric_qecc.yml

@@ -53,6 +53,8 @@ relations:
       detail: 'Random Clifford deformation can improve performance of surface codes against biased noise \cite{arxiv:2201.07802,arxiv:2211.02116}.'
     - code_id: xysurface
       detail: 'XY surface codes perform well against biased noise \cite{arxiv:1708.08474}.'
+    - code_id: xyz_product
+      detail: 'XYZ product codes can be used to protect against biased noise \cite{arxiv:2408.03123}.'
     - code_id: xyz_color
       detail: 'XYZ color codes perform well against biased noise \cite{arxiv:2203.16534}.'
     - code_id: twisted_xzzx

codes/quantum/properties/block/block_quantum.yml

@@ -56,7 +56,7 @@ protection: |
 
   \begin{defterm}{Quantum GV bound}
   \label{topic:quantum-gv-bound}
-  The \hyperref[topic:quantum-gv-bound]{quantum GV bound} \cite{doi:10.1109/TIT.2004.838088} (see also Refs. \cite{arxiv:quant-ph/9602022,arxiv:quant-ph/9906131,doi:10.1109/18.959288,doi:10.1016/j.jmaa.2007.08.023}) for Galois qudits states that a \hyperref[topic:quantum-weight-enumerator]{pure} \([[n,k,d]]_q\) Galois-qudit stabilizer code exists if 
+  The \hyperref[topic:quantum-gv-bound]{quantum GV bound} \cite{doi:10.1109/TIT.2004.838088} (see also Refs. \cite{arxiv:quant-ph/9602022,arxiv:quant-ph/9906131,doi:10.7907/m0xg-zs21,doi:10.1109/18.959288,doi:10.1016/j.jmaa.2007.08.023}) for Galois qudits states that a \hyperref[topic:quantum-weight-enumerator]{pure} \([[n,k,d]]_q\) Galois-qudit stabilizer code exists if 
   \begin{align}
     \frac{q^{n-k+2}-1}{q^{2}-1}>\sum_{j=1}^{d-1}(q^{2}-1)^{j-1}\binom{n}{j}~.
   \end{align}

codes/quantum/properties/block/topological/topological_abelian.yml

@@ -57,20 +57,11 @@ relations:
   parents:
     - code_id: topological
   cousins:
-    - code_id: hamiltonian
-      detail: |
-        Subsystem stabilizer code Hamiltonians described by an Abelian anyon theory do not always realize the corresponding anyonic topological order in their ground-state subspace and may exhibit a rich phase diagram.
-        For example, the Kitaev honeycomb Hamiltonian admits the anyon theories of the 16-fold way, i.e., all minimal modular extensions of the \(\mathbb{Z}_2^{(1)}\) Abelian non-chiral non-modular anyon theory \cite{arxiv:cond-mat/0506438}\cite[Footnote 25]{arxiv:2211.03798}.
     - code_id: walker_wang
       detail: 'Any Abelian anyon theory \(A\) can be realized at one of the surfaces of a 3D Walker-Wang model whose underlying theory is an Abelian TQD containing \(A\) as a subtheory \cite{arxiv:1907.02075,arxiv:2202.05442}\cite[Appx. H]{arxiv:2211.03798}.'
     - code_id: 3d_stabilizer
       detail: 'Qubit 3D stabilizer codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code \cite{arxiv:1908.08049}.'
-    - code_id: translationally_invariant_subsystem
-      detail: |
-        All 2D Abelian bosonic topological orders can be realized as modular-qudit lattice subsystem codes by starting with an Abelian quantum double model (slightly different from that of Ref. \cite{arxiv:2112.11394}) along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:gauging-out]{gauging out} certain bosonic anyons \cite{arxiv:2211.03798}.
-        The stabilizer generators of the new subsystem code may no longer be geometrically local.
-        Non-Abelian topological orders are purported not to be realizable with Pauli stabilizer codes \cite{arxiv:1605.03601}.
-
+
 
 # Begin Entry Meta Information
 _meta:

codes/quantum/properties/subsystem/translationally_invariant_subsystem.yml

@@ -19,6 +19,7 @@ description: |
   On an infinite lattice, its gauge and stabilizer groups are generated by few-site Pauli operators and their translations, in which case the code is called \textit{translationally invariant subsystem code}.
   Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional versions, in which case the stabilizer group may no longer be generated by few-site Pauli operators.
   Lattice defects and boundaries between different codes can also be introduced.
+  Lattice subsystem stabilizer code Hamiltonians described by an Abelian anyon theory do not always realize the corresponding anyonic topological order in their ground-state subspace and may exhibit a rich phase diagram.
 
 features:
   rate: |
@@ -43,6 +44,12 @@ relations:
   cousins:
     - code_id: translationally_invariant_stabilizer
       detail: 'Lattice subsystem codes reduce to lattice stabilizer codes when there are no gauge qudits. The former (latter) is required to admit few-site gauge-group (stabilizer-group) generators on a lattice with boundary conditions.'
+    - code_id: topological_abelian
+      detail: |
+        All 2D Abelian bosonic topological orders can be realized as modular-qudit lattice subsystem codes by starting with an Abelian quantum double model (slightly different from that of Ref. \cite{arxiv:2112.11394}) along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:gauging-out]{gauging out} certain bosonic anyons \cite{arxiv:2211.03798}.
+        The stabilizer generators of the new subsystem code may no longer be geometrically local.
+        Lattice subsystem stabilizer code Hamiltonians described by an Abelian anyon theory do not always realize the corresponding anyonic topological order in their ground-state subspace and may exhibit a rich phase diagram.
+        Non-Abelian topological orders are purported not to be realizable with Pauli stabilizer codes \cite{arxiv:1605.03601}.
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/subsystem/topological/kitaev_honeycomb.yml

@@ -48,6 +48,8 @@ relations:
       During this process, the square lattice is effectively expanded to a hexagonal lattice \cite[Fig. 12]{arxiv:2211.03798}.'
     - code_id: hexagonal
       detail: 'The Kitaev honeycomb model is defined on the honeycomb lattice.'
+    - code_id: topological
+      detail: 'The Kitaev honeycomb model realizes all anyon theories of the 16-fold way, i.e., all minimal modular extensions of the \(\mathbb{Z}_2^{(1)}\) anyon theory \cite{arxiv:cond-mat/0506438}\cite[Footnote 25]{arxiv:2211.03798}. This includes the (non-Abelian) Ising-anyon topological order \cite{arxiv:cond-mat/0506438} (a.k.a. \(p+ip\) superconducting phase \cite{arxiv:1104.5485}) as well as Abelian \(\mathbb{Z}_2\) topological order.'
 
 
 # Begin Entry Meta Information