branching_mera

codes/quantum/properties/block/tensor_network/quantum_lego.yml

@@ -6,17 +6,18 @@
 code_id: quantum_lego
 
 name: 'Quantum Lego code'
-introduced: '\cite{arxiv:2009.10329,arxiv:2109.08158,arxiv:2109.11996,arxiv:2308.05152}'
+introduced: '\cite{arxiv:1312.4578,arxiv:2009.10329,arxiv:2109.08158,arxiv:2109.11996,arxiv:2308.05152}'
 
 alternative_names:
-  - 'Local tensor-network code'
+  - 'Tensor-network code'
 # 2109.11996
 
 #  Code constructed using the quantum LEGO method, which combines multiple codes that have been converted into tensors by tying together the input and outputs of those codes, in a way stacking them similar to LEGOs.
 
 description: |
   Block quantum code constructed using a tensor-network-based graphical framework from \textit{quantum Lego blocks}, which are smaller quantum codes over qubits or qudits.
   The class of codes constructed using the framework depends on the choice of atomic Lego blocks.
+  The identification of encoding circuits with tensor networks was first made in Ref. \cite{arxiv:1312.4578}.
 
   The individual Lego blocks and resulting quantum Lego codes can be stabilizer \cite{arxiv:2009.10329,arxiv:2109.11996} or non-stabilizer \cite{arxiv:2109.08158,arxiv:2308.05152}.
   They need not be isometries, meaning that this class of codes generalizes \hyperref[code:block_perfect]{planar-perfect tensor}-network codes.

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

@@ -32,6 +32,8 @@ description: |
 
   There are three types of \(\mathbb{Z}_2\) topological orders in 3D: one with bosonic charge and loop excitations (BcBl) and two with fermionic charge excitations and bosonic (FcBl) and fermionic (FcFl) loop excitations, respectively \cite{arxiv:2011.11165,arxiv:2110.14654}.
   There exists an invariant that distinguishes these \cite{arxiv:2110.14654}.
+  A similar pattern follows in higher dimensions.
+
 
 features:
   encoders:

codes/quantum/qubits/ea_stabilizer/quantum_polar.yml

@@ -25,6 +25,9 @@ protection: 'Protects against Pauli noise and erasures.'
 features:
   rate: 'The rate approaches the symmetric coherent information of arbitrary quantum channels \cite{arxiv:1201.2906}.'
 
+  encoders:
+    - 'Encoding circuits can be viewed as branching-tree tensor networks \cite{arxiv:1312.4578}.'
+
   decoders:
     - 'Quantum successive-cancellation list decoder (SCL-E) for quantum polar codes that do not need entanglement assistance \cite{arxiv:2304.04743}.'
 
@@ -41,6 +44,8 @@ relations:
       A variant of quantum polar codes exists that does not require entanglement assistance \cite{arxiv:1307.1136}.'
     - code_id: polar
       detail: 'Without entanglement assistance, quantum polar codes are just CSS codes constructed out of polar codes.'
+    - code_id: quantum_lego
+      detail: 'Quantum polar encoding circuits can be viewed as branching-tree tensor networks \cite{arxiv:1312.4578}.'
 
 
 # Begin Entry Meta Information

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

@@ -20,6 +20,7 @@ description: |-
 features:
   encoders:
     - 'Encoding is efficient and uses only Clifford gates. Some encoders yield \textit{catastrophic} errors, i.e., errors that require a circuit of infinite depth to correct \cite[Def. 4.1]{arxiv:quant-ph/0401134}.'
+    - 'Encoding circuits can be viewed as matrix-product-state tensor networks \cite{arxiv:1312.4578}.'
   decoders:
     - 'ML decoder \cite{arxiv:quant-ph/0304189}.'
 
@@ -32,8 +33,11 @@ relations:
   parents:
     - code_id: qubit_stabilizer
     - code_id: translationally_invariant_stabilizer
-      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}.'
+      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}.
+    - code_id: quantum_lego
+      detail: 'Quantum convolutional encoding circuits can be viewed as matrix-product-state tensor networks \cite{arxiv:1312.4578}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/css/quantum_parity.yml

@@ -42,7 +42,7 @@ protection: 'Has distance \(d=\min(m_1,m_2)\).'
 
 features:
   encoders:
-    - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294}.'
+    - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294} and tree tensor networks \cite{arxiv:1312.4578}.'
 
 realizations:
   - 'The \([[m^2,1,m]]\) codes for \(m\leq 7\) have been realized in trapped-ion quantum devices \cite{arxiv:2104.01205}.'
@@ -57,6 +57,8 @@ relations:
     - code_id: generalized_shor
     - code_id: group_quantum_parity
       detail: 'A \([[m_1 m_2,1,\min(m_1,m_2)]]_G\) group-based QPC reduces to a QPC for \(G=\mathbb{Z}_2\).'
+    - code_id: quantum_lego
+      detail: 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294} and tree tensor networks \cite{arxiv:1312.4578}.'
   cousins:
     - code_id: bacon_shor
       detail: 'Bacon-Shor codes reduce to QPCs when all \(X\)-type gauge generators are fixed \cite[pg. 6]{arxiv:1809.01193}.'

codes/quantum/qubits/stabilizer/holographic/branching_mera.yml

@@ -0,0 +1,32 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: branching_mera
+physical: qubits
+logical: qubits
+
+name: 'Branching MERA code'
+introduced: '\cite{arxiv:1312.4575,arxiv:1312.4578,doi:10.1109/ISIT.2014.6874999}'
+
+description: |
+  Qubit stabilizer code whose encoding circuit corresponds to a branching MERA tensor network \cite{arxiv:1210.1895}.
+
+
+relations:
+  parents:
+    - code_id: qubit_stabilizer
+    - code_id: quantum_lego
+      detail: 'Encoders for branching MERA codes are related to branching MERA tensor networks \cite{arxiv:1312.4575,arxiv:1312.4578}.'
+  cousins:
+    - code_id: polar
+      detail: 'Classical versions of branching MERA codes can be thought of as extensions of polar codes \cite{arxiv:1312.4575,doi:10.1109/ISIT.2014.6874999}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-10'

codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_13_surface.yml

@@ -37,4 +37,6 @@ _meta:
   # Change log - most recent first
   changelog:
     - user_id: VictorVAlbert
-      date: '2024-04-26'
+      date: '2024-07-10'
+    - user_id: nathanan
+      date: '2024-07-10'

codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml

@@ -20,6 +20,7 @@ alternative_names:
 description: |
   A generalization of the Kitaev surface code defined on a 4D lattice.
   The code is called a \((2,2)\) toric code because it admits 2D \(Z\)-type and 2D \(X\)-type logical operators.
+  Both types of operators create 1D (i.e., loop) excitations at their edges.
   The code serves as a self-correcting quantum memory \cite{arxiv:quant-ph/0110143,arxiv:0811.0033}.
 
   \textit{Loop toric code} often either refers to the construction on