From 3f458b64511a04d829affceedab49d93a439c2d3 Mon Sep 17 00:00:00 2001
From: "Victor V. Albert" <valbert4@gmail.com>
Date: Sat, 27 Jan 2024 23:06:25 -0500
Subject: [PATCH] 2d + 3d stabilizer

---
 .../groups/topological/quantum_double.yml     |  2 -
 .../topological/topological_abelian.yml       |  2 -
 .../properties/hamiltonian/self_correct.yml   |  2 +-
 .../translationally_invariant_stabilizer.yml  | 82 -------------------
 .../topological_stabilizer/2d_stabilizer.yml  | 39 +++++++++
 .../topological_stabilizer/3d_stabilizer.yml  | 36 ++++++++
 .../topological_stabilizer}/fracton.yml       | 10 +--
 .../translationally_invariant_stabilizer.yml  | 61 ++++++++++++++
 codes/quantum/qubits/dynamic_gen/da/da.yml    |  2 +
 codes/quantum/qubits/mbqc/rbh.yml             |  1 +
 .../stabilizer/qldpc/sc_qldpc/sc_qldpc.yml    |  2 +-
 .../qubits/stabilizer/quantum_parity.yml      |  3 +-
 .../stabilizer/topological/color/3d_color.yml |  1 +
 .../convolutional/quantum_convolutional.yml   |  3 +-
 .../3d_fermionic_surface.yml                  |  1 +
 .../surface/higher_dim_surface/3d_surface.yml |  1 +
 .../surface/higher_dimensional_surface.yml    |  8 +-
 .../surface/two_dim/surface/surface.yml       |  2 +-
 .../stabilizer/topological/three_fermion.yml  |  3 +-
 .../topological/quantum_double_abelian.yml    |  2 +-
 .../qudits/topological/tqd_abelian.yml        |  3 +
 .../qldpc/galois_topological.yml              |  4 +-
 22 files changed, 166 insertions(+), 104 deletions(-)
 rename codes/quantum/{qudits/subsystem => properties/block}/topological/topological_abelian.yml (99%)
 delete mode 100644 codes/quantum/properties/stabilizer/qldpc/translationally_invariant_stabilizer.yml
 create mode 100644 codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml
 create mode 100644 codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml
 rename codes/quantum/properties/{block/topological => stabilizer/topological_stabilizer}/fracton.yml (66%)
 create mode 100644 codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml

diff --git a/codes/quantum/groups/topological/quantum_double.yml b/codes/quantum/groups/topological/quantum_double.yml
index 1ba40f090..209e7d206 100644
--- a/codes/quantum/groups/topological/quantum_double.yml
+++ b/codes/quantum/groups/topological/quantum_double.yml
@@ -44,8 +44,6 @@ relations:
       detail: 'Quantum-double Hamiltonians can be expressed in terms of \(X\)- and \(Z\)-type operators of group-GKP codes; see \cite[Sec. 3.3]{arxiv:2111.12096}.'
     - code_id: tqd
       detail: 'The anyon theory corresponding to a quantum-double code is a TQD with trivial cocycle. These models realize local topological order (LTO) \cite{arxiv:2309.13440}.'
-    - code_id: string_net
-      detail: 'String-net model reduces to the quantum-double model for group categories.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qudits/subsystem/topological/topological_abelian.yml b/codes/quantum/properties/block/topological/topological_abelian.yml
similarity index 99%
rename from codes/quantum/qudits/subsystem/topological/topological_abelian.yml
rename to codes/quantum/properties/block/topological/topological_abelian.yml
index a1008efed..b4e4c0d3b 100644
--- a/codes/quantum/qudits/subsystem/topological/topological_abelian.yml
+++ b/codes/quantum/properties/block/topological/topological_abelian.yml
@@ -4,8 +4,6 @@
 #######################################################
 
 code_id: topological_abelian
-physical: qudits
-logical: qudits
 
 name: 'Abelian topological code'
 #introduced: ''
diff --git a/codes/quantum/properties/hamiltonian/self_correct.yml b/codes/quantum/properties/hamiltonian/self_correct.yml
index 3dec78322..f11c95d47 100644
--- a/codes/quantum/properties/hamiltonian/self_correct.yml
+++ b/codes/quantum/properties/hamiltonian/self_correct.yml
@@ -37,7 +37,7 @@ relations:
     - code_id: symmetry_protected_self_correct
       detail: 'A self-correcting quantum memory does not require symmetry for self correction.'
   cousins:
-    - code_id: translationally_invariant_stabilizer
+    - code_id: 3d_stabilizer
       detail: '3D translationally-invariant qubit stabilizer code families with constant \(k\) support logical string operators and thus cannot be self-correcting \cite{arXiv:1103.1885}. For non-constant \(k\), such families can support at most a logarithmic energy barrier \cite{arXiv:1101.1962}.'
     - code_id: higher_dimensional_surface
       detail: 'The 4D toric code is a self-correcting quantum memory \cite{arXiv:quant-ph/0110143,arXiv:0811.0033}.'
diff --git a/codes/quantum/properties/stabilizer/qldpc/translationally_invariant_stabilizer.yml b/codes/quantum/properties/stabilizer/qldpc/translationally_invariant_stabilizer.yml
deleted file mode 100644
index 5ceab6b71..000000000
--- a/codes/quantum/properties/stabilizer/qldpc/translationally_invariant_stabilizer.yml
+++ /dev/null
@@ -1,82 +0,0 @@
-#######################################################
-## This is a code entry in the error correction zoo. ##
-##       https://github.com/errorcorrectionzoo       ##
-#######################################################
-
-code_id: translationally_invariant_stabilizer
-# includes both Galois and modular
-
-name: 'Translationally invariant stabilizer code'
-introduced: '\cite{arXiv:1101.1962,arXiv:1204.1063,doi:10.7907/GCYW-ZE58}'
-
-alternative_names:
-  - 'Topological stabilizer code'
-
-description: |
-  A geometrically local qubit, modular-qudit, or Galois-qudit stabilizer code with qudits organized on a lattice modeled by the additive group \(\mathbb{Z}^D\) for spatial dimension \(D\) such that each lattice point, referred to as a site,
-  contains \(m\) qudits of dimension \(q\).
-  The stabilizer group of the translationally invariant code is generated by site-local Pauli operators and their translations.
-  Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional codes.
-  Infinite dimensional formulations are also possible, with the 1D lattice version reducing to quantum convolutional codes.
-
-  \begin{defterm}{Pauli-to-polynomial mapping}
-  \label{topic:quantum-polynomial-mapping}
-  A single-qudit Pauli operator can be specified by the lattice coordinate of the site and the symplectic vector
-  representation of the Pauli operator within the site.
-  In an extension of the sympletic representation, each lattice coordinate can be represented by a Laurent monomial of \(D\) formal variables. For example, when \(D=2\) and \(m=1\), the product of an \(X\) acting on the qubit at lattice coordinate \((-1,2)\) and a \(Z\) acting on the qubit at \((1,0)\) can be represented by the vector \( (x^{-1} y^2 | x) \). The multiplicative group of finitely supported Pauli operators modulo phase factors on the lattice of dimension \(D\) with \(m\) prime-dimensional qubits per site is isomorphic to the additive group of Laurent polynomial column vectors of length \(2m\) in \(D\) formal variables (see Ref. \cite{arXiv:1607.01387} and Sec. IV of Ref. \cite{arXiv:1812.01625}).
-  \end{defterm}
-
-  Translationally-invariant prime-qudit (\(q=p\)) stabilizer codes have been classified in dimensions \(D\in\{1,2\}\), up to equivalence under local constant-depth Clifford circuits. Any 1D (2D) code can be converted to several copies of the 1D repetition code (prime-qudit 2D surface code) along with some trivial codes \cite{arXiv:1607.01387} (\cite{arXiv:1812.11193}). Three-dimensional qubit codes can be characterized by four
-  coarse classes \cite{arXiv:1908.08049}:
-
-  1. \textit{Abelian topological phase}: Excitations are mobile in all 3 dimensions, as is typical in a topological code. Such codes are conjectured to be equivalent to a \(\mathbb{Z}_2\) gauge theory, i.e., multiple copies of the 3D surface code or its variant where the charge excitation is a fermion.
-
-  2. \textit{Foliated type-I fracton phase}: Excitations are mobile in less than 3 dimensions, but codes can be grown by \textit{foliation}, i.e., stacking copies of the 2D surface code.
-
-  3. \textit{Fractal type-I fracton phase}: Excitations are mobile in less than 3 dimensions, and codes are not foliated.
-
-  4. \textit{Type-II fracton phase}: Excitations are not mobile in any dimension and there are no string operators.
-
-#The code is specified by a stabilizer group that is generated by site-local Pauli operators and is translationally invariant with respect to the lattice.
-#As an example with \(p = 2\) and \(D = 3\), \(P(1, 2, 3; e_1)P(-1, 2, 4; e_{q+2})\) is the Pauli operator that applies \(X\) to
-#  qubit \(1\) of lattice point \((1, 2, 3)\) and applies \(Z\) to qubit \(2\) of lattice point \((-1, 2, 4)\). This operator can be
-#  equivalently expressed by the Laurent polynomial \(x_1x_2^2x_3^3e_1 + x_1^{-1}x_2^2x_3^4e_{q+2}\).
-
-features:
-  decoders:
-    - 'Standard stabilizer-based error correction can be performed for translationally invariant stabilizer codes even in the presence of perturbations to the codespace \cite{arxiv:2401.06300}.'
-    - 'Clustering decoder \cite{doi:10.7907/AHMQ-EG82,arXiv:1112.3252}.'
-    - 'Tensor-network based decoder for 2D codes subject to correlated noise \cite{arxiv:1809.10704}.'
-    - 'Quantum neural-network (QNN) decoder \cite{arxiv:2401.06300}.'
-
-relations:
-  parents:
-    - code_id: qldpc
-      detail: 'Translationally-invariant stabilizer codes are geometrically local.'
-    - code_id: quantum_quasi_cyclic
-      detail: 'Translationally-invariant stabilizer codes are invariant under translations by a unit cell.'
-  cousins:
-    - code_id: qudit_stabilizer
-      detail: 'Modular-qudit stabilizer codes can be thought of as translationally-invariant stabilizer codes for dimension \(D = 0\), with the lattice consisting of a single site with some number of qudits.'
-    - code_id: surface
-      detail: 'Translation-invariant 2D qubit topological stabilizer codes are equivalent to several copies of the Kitaev surface code via a local constant-depth Clifford circuit \cite{arXiv:1103.4606,arXiv:1107.2707,arXiv:1607.01387}.
-      There exists an algorithm with which one can determine the fusion and braiding rules of a 2D translationally invariant qubit code, and decompose the given code into copies of the surface code \cite{arxiv:2312.11170}.'
-    - code_id: quantum_double_abelian
-      detail: 'Translation-invariant 2D prime-qudit topological stabilizer codes are equivalent to several copies of the prime-qudit surface code via a local constant-depth Clifford circuit \cite{arxiv:1812.11193}.'
-    - code_id: tqd_abelian
-      detail: 'Translationally-invariant stabilizer codes can realize 2D modular gapped Abelian bosonic topological orders \cite{arxiv:2211.03798}.
-      Conversely, Abelian TQD codes need not be translationally invariant, and can realize multiple topological phases on one lattice.'
-    - code_id: fracton
-      detail: 'Translationally-invariant stabilizer codes can realize fracton orders. Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.'
-    - code_id: holographic
-      detail: '2D topological stabilizer codes admit a bulk-boundary correspondence similar to that of holographic codes, namely, the boundary Hilbert space of the former cannot be realized via local degrees of freedom \cite{arxiv:2312.04617}.'
-
-
-# Begin Entry Meta Information
-_meta:
-  # Change log - most recent first
-  changelog:
-    - user_id: VictorVAlbert
-      date: '2022-05-15'
-    - user_id: TonyLau
-      date: '2022-04-02'
diff --git a/codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml b/codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml
new file mode 100644
index 000000000..5e8d9271c
--- /dev/null
+++ b/codes/quantum/properties/stabilizer/topological_stabilizer/2d_stabilizer.yml
@@ -0,0 +1,39 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: 2d_stabilizer
+# includes both Galois and modular
+
+name: '2D topological stabilizer code'
+
+description: |
+  Translationally invariant stabilizer code in two spatial dimensions.
+
+  Any prime-qudit code can be converted to several copies of the prime-qudit 2D surface code along with some trivial codes \cite{arXiv:1812.11193}.
+
+features:
+  decoders:
+    - 'Tensor-network based decoder for 2D codes subject to correlated noise \cite{arxiv:1809.10704}.'
+    - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2401.06300}.'
+
+relations:
+  parents:
+    - code_id: translationally_invariant_stabilizer
+  cousins:
+    - code_id: surface
+      detail: 'Translation-invariant 2D qubit topological stabilizer codes are equivalent to several copies of the Kitaev surface code via a local constant-depth Clifford circuit \cite{arXiv:1103.4606,arXiv:1107.2707,arXiv:1607.01387}.
+      There exists an algorithm with which one can determine the fusion and braiding rules of a 2D translationally invariant qubit code, and decompose the given code into copies of the surface code \cite{arxiv:2312.11170}.'
+    - code_id: quantum_double_abelian
+      detail: 'Translation-invariant 2D prime-qudit topological stabilizer codes are equivalent to several copies of the prime-qudit surface code via a local constant-depth Clifford circuit \cite{arxiv:1812.11193}.'
+    - code_id: holographic
+      detail: '2D topological stabilizer codes admit a bulk-boundary correspondence similar to that of holographic codes, namely, the boundary Hilbert space of the former cannot be realized via local degrees of freedom \cite{arxiv:2312.04617}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-01-27'
diff --git a/codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml b/codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml
new file mode 100644
index 000000000..c7c0a43c0
--- /dev/null
+++ b/codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml
@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: 3d_stabilizer
+# includes both Galois and modular
+
+name: '3D topological stabilizer code'
+
+description: |
+  Translationally invariant stabilizer code in three spatial dimensions.
+
+  Three-dimensional qubit codes can be characterized by four
+  coarse classes \cite{arXiv:1908.08049}:
+
+  1. \textit{Abelian topological phase}: Excitations are mobile in all 3 dimensions, as is typical in a topological code. Such codes are conjectured to be equivalent to a \(\mathbb{Z}_2\) gauge theory, i.e., multiple copies of the 3D surface code or its variant where the charge excitation is a fermion.
+
+  2. \textit{Foliated type-I fracton phase}: Excitations are mobile in less than 3 dimensions, but codes can be grown by \textit{foliation}, i.e., stacking copies of the 2D surface code.
+
+  3. \textit{Fractal type-I fracton phase}: Excitations are mobile in less than 3 dimensions, and codes are not foliated.
+
+  4. \textit{Type-II fracton phase}: Excitations are not mobile in any dimension and there are no string operators.
+
+
+relations:
+  parents:
+    - code_id: translationally_invariant_stabilizer
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-01-27'
diff --git a/codes/quantum/properties/block/topological/fracton.yml b/codes/quantum/properties/stabilizer/topological_stabilizer/fracton.yml
similarity index 66%
rename from codes/quantum/properties/block/topological/fracton.yml
rename to codes/quantum/properties/stabilizer/topological_stabilizer/fracton.yml
index b9852c28f..d5dfca005 100644
--- a/codes/quantum/properties/block/topological/fracton.yml
+++ b/codes/quantum/properties/stabilizer/topological_stabilizer/fracton.yml
@@ -6,18 +6,16 @@
 code_id: fracton
 # includes Galois and modular
 
-name: 'Fracton code'
+name: 'Fracton stabilizer code'
 #introduced: '\cite{arXiv:quant-ph/9705052}'
 
-description: 'A code whose codewords make up the ground-state space of a fracton-phase Hamiltonian.'
+description: 'A 3D translationally invariant stabilizer code whose codewords make up the ground-state space of a Hamiltonian in a fracton phase.'
 
-protection: ''
-# Can expound on normalizer etc
 
 relations:
   parents:
-    - code_id: qldpc
-      detail: 'Fracton codes admit geometrically local stabilizer generators on a cubic lattice.'
+    - code_id: 3d_stabilizer
+      detail: '3D stabilizer codes can realize fracton orders. Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.'
   cousins:
     - code_id: topological
       detail: 'Fracton phases can be understood as topological defect networks, meaning that they can be described in the language of topological quantum field theory with defects \cite{arXiv:2002.05166,arxiv:2112.14717}.'
diff --git a/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml b/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml
new file mode 100644
index 000000000..a5c7ef1f7
--- /dev/null
+++ b/codes/quantum/properties/stabilizer/topological_stabilizer/translationally_invariant_stabilizer.yml
@@ -0,0 +1,61 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: translationally_invariant_stabilizer
+# includes both Galois and modular
+
+name: 'Lattice stabilizer code'
+introduced: '\cite{arXiv:1101.1962,arXiv:1204.1063,doi:10.7907/GCYW-ZE58}'
+# geometrically local would also cover hyperbolic, Euclidean overlaps with CSS
+
+description: |
+  A geometrically local qubit, modular-qudit, or Galois-qudit stabilizer code with qudits organized on a lattice modeled by the additive group \(\mathbb{Z}^D\) for spatial dimension \(D\).
+  If the stabilizer group is generated by site-local Pauli operators and their translations, then the code is called \textit{translationally invariant stabilizer code}.
+  Boundary conditions have to be imposed on the lattice in order to obtain finite-dimensional codes.
+  Lattice defects and boundaries between different codes can also be introduced.
+  It is possible to formulate a thermodynamic limit for lattice codes, with the 1D lattice version reducing to quantum convolutional codes.
+
+  Translationally-invariant prime-qudit (\(q=p\)) stabilizer codes with \(m\) qudits per unit cell have been classified in dimensions \(D\in\{1,2\}\) in the thermodynamic limit, up to equivalence under local constant-depth Clifford circuits.
+  Any 1D (2D) code can be converted to several copies of the 1D repetition code (prime-qudit 2D surface code) along with some trivial codes \cite{arXiv:1607.01387} (\cite{arXiv:1812.11193}).
+  See 3D topological stabilizer code entry for the 3D classification.
+
+  \begin{defterm}{Pauli-to-polynomial mapping}
+  \label{topic:quantum-polynomial-mapping}
+  A single-qudit Pauli operator can be specified by the lattice coordinate of the site and the symplectic vector
+  representation of the Pauli operator within the site.
+  In an extension of the sympletic representation, each lattice coordinate can be represented by a Laurent monomial of \(D\) formal variables. For example, when \(D=2\) and \(m=1\), the product of an \(X\) acting on the qubit at lattice coordinate \((-1,2)\) and a \(Z\) acting on the qubit at \((1,0)\) can be represented by the vector \( (x^{-1} y^2 | x) \). The multiplicative group of finitely supported Pauli operators modulo phase factors on the lattice of dimension \(D\) with \(m\) prime-dimensional qubits per site is isomorphic to the additive group of Laurent polynomial column vectors of length \(2m\) in \(D\) formal variables (see Ref. \cite{arXiv:1607.01387} and Sec. IV of Ref. \cite{arXiv:1812.01625}).
+  \end{defterm}
+
+
+#The code is specified by a stabilizer group that is generated by site-local Pauli operators and is translationally invariant with respect to the lattice.
+#As an example with \(p = 2\) and \(D = 3\), \(P(1, 2, 3; e_1)P(-1, 2, 4; e_{q+2})\) is the Pauli operator that applies \(X\) to
+#  qubit \(1\) of lattice point \((1, 2, 3)\) and applies \(Z\) to qubit \(2\) of lattice point \((-1, 2, 4)\). This operator can be
+#  equivalently expressed by the Laurent polynomial \(x_1x_2^2x_3^3e_1 + x_1^{-1}x_2^2x_3^4e_{q+2}\).
+
+features:
+  decoders:
+    - 'Clustering decoder \cite{doi:10.7907/AHMQ-EG82,arXiv:1112.3252}.'
+    - 'Quantum neural-network (QNN) decoder \cite{arxiv:2401.06300}.'
+
+relations:
+  parents:
+    - code_id: qldpc
+      detail: 'Lattice stabilizer codes are geometrically local.'
+    - code_id: quantum_quasi_cyclic
+      detail: 'Lattice stabilizer codes are invariant under translations by a lattice unit cell.'
+
+
+    # - code_id: qudit_stabilizer
+    #   detail: 'Modular-qudit stabilizer codes can be thought of as lattice stabilizer codes for dimension \(D = 0\), with the lattice consisting of a single site with some number of qudits.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2022-05-15'
+    - user_id: TonyLau
+      date: '2022-04-02'
diff --git a/codes/quantum/qubits/dynamic_gen/da/da.yml b/codes/quantum/qubits/dynamic_gen/da/da.yml
index a7c97bb67..48f787712 100644
--- a/codes/quantum/qubits/dynamic_gen/da/da.yml
+++ b/codes/quantum/qubits/dynamic_gen/da/da.yml
@@ -45,6 +45,8 @@ relations:
       detail: 'One of the instantaneous stabilizer codes of the 2D DA color code are stacks of toric/surface codes'
     - code_id: topological_abelian
       detail: 'Useful measurement sequences of DA Floquet codes can be extracted from topological quantum field theory \cite{arXiv:2307.10353}.'
+    - code_id: translationally_invariant_stabilizer
+      detail: 'DA codes are defined on 2D and 3D lattices, but they are not conventional stabilizer codes in that they use code switching for error correction and gates.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qubits/mbqc/rbh.yml b/codes/quantum/qubits/mbqc/rbh.yml
index cfa7de0c9..37f867004 100644
--- a/codes/quantum/qubits/mbqc/rbh.yml
+++ b/codes/quantum/qubits/mbqc/rbh.yml
@@ -41,6 +41,7 @@ features:
 relations:
   parents:
     - code_id: cluster_state
+    - code_id: 3d_stabilizer
     - code_id: walker_wang
       detail: 'The Walker-Wang model code reduces to the RBH cluster-state code when the input category \(\mathcal{C}\) is that of the surface code \cite[Sec. V.A]{arxiv:2011.04693}.'
   cousins:
diff --git a/codes/quantum/qubits/stabilizer/qldpc/sc_qldpc/sc_qldpc.yml b/codes/quantum/qubits/stabilizer/qldpc/sc_qldpc/sc_qldpc.yml
index 3ba2c604c..4b61831cf 100644
--- a/codes/quantum/qubits/stabilizer/qldpc/sc_qldpc/sc_qldpc.yml
+++ b/codes/quantum/qubits/stabilizer/qldpc/sc_qldpc/sc_qldpc.yml
@@ -174,7 +174,7 @@ relations:
   parents:
     - code_id: qubit_stabilizer
     - code_id: translationally_invariant_stabilizer
-      detail: 'Stabilizer generator matrices of SC-QLDPC codes on infinite-length chains or grids define a class of translationally-invariant stabilizer codes.'
+      detail: 'Stabilizer generator matrices of SC-QLDPC codes on infinite-length chains or grids define a class of lattice stabilizer codes.'
   cousins:
     - code_id: sc_ldpc
       detail: 'SC-QLDPC code stabilizer-generator matrices have similar block form as the parity-check matrices of SC-LDPC codes.'
diff --git a/codes/quantum/qubits/stabilizer/quantum_parity.yml b/codes/quantum/qubits/stabilizer/quantum_parity.yml
index 6c06d674e..773b79619 100644
--- a/codes/quantum/qubits/stabilizer/quantum_parity.yml
+++ b/codes/quantum/qubits/stabilizer/quantum_parity.yml
@@ -36,7 +36,6 @@ notes:
 relations:
   parents:
     - code_id: generalized_shor
-    - code_id: translationally_invariant_stabilizer
     - code_id: quantum_concatenated
       detail: 'A QPC is a concatenation of a phase-flip repetition code with a bit-flip repetition code.'
   cousins:
@@ -45,6 +44,8 @@ relations:
     - code_id: majorana_stab
       detail: 'QPCs for \(m_1=m_2\) can be conveniantly expressed in terms of mutually commuting Majorana operators \cite{arxiv:quant-ph/0003137}.'
 
+#     - code_id: translationally_invariant_stabilizer
+# Doesn't seem to be since stab gens can be arbitrarily large
 
 # Begin Entry Meta Information
 _meta:
diff --git a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
index 43b808a55..c9d41be47 100644
--- a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
+++ b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
@@ -25,6 +25,7 @@ features:
 relations:
   parents:
     - code_id: color
+    - code_id: 3d_stabilizer
     - code_id: topological_abelian
     - code_id: quantum_triorthogonal
   cousins:
diff --git a/codes/quantum/qubits/stabilizer/topological/convolutional/quantum_convolutional.yml b/codes/quantum/qubits/stabilizer/topological/convolutional/quantum_convolutional.yml
index f14b8259f..5393c7dfb 100644
--- a/codes/quantum/qubits/stabilizer/topological/convolutional/quantum_convolutional.yml
+++ b/codes/quantum/qubits/stabilizer/topological/convolutional/quantum_convolutional.yml
@@ -32,7 +32,8 @@ relations:
   parents:
     - code_id: qubit_stabilizer
     - code_id: translationally_invariant_stabilizer
-      detail: 'Quantum convolutional codes are translationally-invariant stabilizer codes on an semi-infinite or infinite lattice in one dimension \cite{arxiv:1305.6973}. Some notions may be extendable to non-stabilizer codes \cite[Sec. 4]{arxiv:quant-ph/0401134}.'
+      detail: 'Quantum convolutional codes are lattice stabilizer codes on an semi-infinite or infinite lattice in one dimension \cite{arxiv:1305.6973}. Some notions may be extendable to non-stabilizer codes \cite[Sec. 4]{arxiv:quant-ph/0401134}.
+      Any prime-qudit code can be converted using a constant-depth Clifford circuit to several copies of the 1D repetition code along with some trivial codes \cite{arXiv:1607.01387}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_fermionic_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_fermionic_surface.yml
index 164a26f23..0c25e68d5 100644
--- a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_fermionic_surface.yml
+++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_fermionic_surface.yml
@@ -29,6 +29,7 @@ features:
 relations:
   parents:
     - code_id: higher_dimensional_surface
+    - code_id: 3d_stabilizer
     - code_id: topological_abelian
       detail: 'The 3D Kitaev surface code realizes 3D \(\mathbb{Z}_2\) gauge theory with an emergent fermion.'
 
diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
index 54c25a9ea..b2285990e 100644
--- a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
+++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
@@ -43,6 +43,7 @@ features:
 relations:
   parents:
     - code_id: higher_dimensional_surface
+    - code_id: 3d_stabilizer
     - code_id: topological_abelian
       detail: 'The 3D Kitaev surface code realizes 3D \(\mathbb{Z}_2\) gauge theory.'
   cousins:
diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_dimensional_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_dimensional_surface.yml
index 2aa8e5146..d6cdfacb6 100644
--- a/codes/quantum/qubits/stabilizer/topological/surface/higher_dimensional_surface.yml
+++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_dimensional_surface.yml
@@ -11,13 +11,15 @@ name: 'Generalized surface code'
 introduced: '\cite{arxiv:quant-ph/0110143,doi:10.1201/9781420035377-13,doi:10.1007/978-3-642-01877-0_21}'
 
 description: |
-  Also called the \(D\)\textit{-dimensional surface} or \(D\)\textit{-dimensional toric} code.
-  CSS-type extenstion of the Kitaev surface code to arbitrary \(D\)-dimensional manifolds.
-  The 4D surface code serves as a self-correcting quantum memory, while surface codes in higher dimensions can have distances not possible in lower dimensions.
+  CSS-type extenstion of the Kitaev surface code to arbitrary manifolds.
+  The version on a Euclidean manifold of some fixed dimension is called the \(D\)\textit{-dimensional surface} or \(D\)\textit{-dimensional toric} code.
 
   Given a cellulation of a manifold, qubits are put on \(i\)-dimensional faces, \(X\)-type stabilizers
   are associated with \((i-1)\)-faces, while \(Z\)-type stabilizers are associated with \((i+1)\)-faces.
 
+  The 4D surface code serves as a self-correcting quantum memory, while surface codes in higher dimensions can have distances not possible in lower dimensions.
+
+
 
 features:
   rate: |
diff --git a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml
index 0009f6a38..57c70698c 100644
--- a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml
+++ b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml
@@ -176,7 +176,7 @@ relations:
     - code_id: qudit_surface
       detail: 'The modular-qudit surface code for \(q=2\) reduces to the surface code.'
     - code_id: galois_topological
-      detail: 'The surface code has been extended to Galois qudits.'
+      detail: 'The Galois-qudit surface code for \(q=2\) reduces to the surface code.'
   cousins:
     - code_id: majorana_stab
       detail: 'The Majorana mapping can be used to construct efficient algorithms for simulating rounds of error correction for the surface code \cite{arxiv:1710.02270}.'
diff --git a/codes/quantum/qubits/stabilizer/topological/three_fermion.yml b/codes/quantum/qubits/stabilizer/topological/three_fermion.yml
index 665aa1bb6..49584bd7b 100644
--- a/codes/quantum/qubits/stabilizer/topological/three_fermion.yml
+++ b/codes/quantum/qubits/stabilizer/topological/three_fermion.yml
@@ -12,7 +12,7 @@ short_name: '3F model'
 introduced: '\cite{arxiv:2011.04693}'
 
 description: |
-  A 3D topological code whose low-energy excitations realize the three-fermion anyon theory \cite{arxiv:0712.1377,arxiv:0811.0911,arxiv:1103.4606} and that can be used as a resource state for fault-tolerant MBQC \cite{arxiv:2011.04693}.
+  A 3D topological stabilizer code whose low-energy excitations realize the three-fermion anyon theory \cite{arxiv:0712.1377,arxiv:0811.0911,arxiv:1103.4606} and that can be used as a resource state for fault-tolerant MBQC \cite{arxiv:2011.04693}.
 
 features:
   general_gates:
@@ -23,6 +23,7 @@ features:
 relations:
   parents:
     - code_id: qubit_stabilizer
+    - code_id: 3d_stabilizer
     - code_id: walker_wang
       detail: 'The Walker-Wang model code reduces to the 3F model code when the input category \(\mathcal{C}=3F\) \cite{arxiv:2011.04693}.'
     - code_id: topological_abelian
diff --git a/codes/quantum/qudits/topological/quantum_double_abelian.yml b/codes/quantum/qudits/topological/quantum_double_abelian.yml
index b4c737a67..2e185d5ee 100644
--- a/codes/quantum/qudits/topological/quantum_double_abelian.yml
+++ b/codes/quantum/qudits/topological/quantum_double_abelian.yml
@@ -7,7 +7,7 @@ code_id: quantum_double_abelian
 physical: qudits
 logical: qudits
 
-name: 'Abelian quantum double stabilizer code'
+name: 'Abelian quantum-double stabilizer code'
 introduced: '\cite{arXiv:quant-ph/9707021}'
 
 description: |
diff --git a/codes/quantum/qudits/topological/tqd_abelian.yml b/codes/quantum/qudits/topological/tqd_abelian.yml
index b34a259b5..bc7c33bef 100644
--- a/codes/quantum/qudits/topological/tqd_abelian.yml
+++ b/codes/quantum/qudits/topological/tqd_abelian.yml
@@ -19,6 +19,9 @@ relations:
   parents:
     - code_id: qudit_stabilizer
       detail: 'All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}.'
+    - code_id: 2d_stabilizer
+      detail: 'All Abelian TQD codes can be realized as modular-qudit stabilizer codes by starting with an Abelian quantum double model along with a family of Abelian TQDs that generalize the double semion anyon theory and \hyperref[topic:code-switching]{condensing} certain bosonic anyons \cite{arxiv:2211.03798}.
+      Abelian TQD codes need not be translationally invariant and can realize multiple topological phases on one lattice.'
     - code_id: topological_abelian
       detail: 'Abelian TQDs realize all modular gapped Abelian topological orders \cite{arxiv:2112.11394}.
       Conversely, every Abelian anyon theory is a subtheory of some TQD \cite[Sec. 6.2]{arxiv:2211.03798}.
diff --git a/codes/quantum/qudits_galois/qldpc/galois_topological.yml b/codes/quantum/qudits_galois/qldpc/galois_topological.yml
index b1c3ba544..05e09a6fe 100644
--- a/codes/quantum/qudits_galois/qldpc/galois_topological.yml
+++ b/codes/quantum/qudits_galois/qldpc/galois_topological.yml
@@ -16,8 +16,8 @@ description: |
 relations:
   parents:
     - code_id: galois_css
-    - code_id: topological
-# topological_abelian is modular qudit based, so cousin
+    - code_id: 2d_stabilizer
+    - code_id: topological_abelian
   cousins:
     - code_id: quantum_double_abelian
       detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}; see Sec. 5.3 of Ref. \cite{arxiv:quant-ph/0501074}.