cubic_theory

codes/quantum/qubits/stabilizer/topological/cubic_theory.yml

@@ -0,0 +1,44 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: cubic_theory
+physical: qubits
+logical: qubits
+
+name: 'Cubic theory code'
+introduced: '\cite{arxiv:2405.11719}'
+
+alternative_names:
+  - 'Non-Abelian self-correcting quantum memory'
+  - 'Magic stabilizer code'
+
+description: |
+  A geometrically local commuting-projector code defined on triangulations of lattices in five and higher spatial dimensions. Its code Hamiltonian terms include Pauli-\(Z\) operators and products of Pauli-\(X\) operators and \(CZ\) gates.
+  The Hamiltonian realizes higher-form \(\mathbb{Z}_2^3\) gauge theories whose excitations obey non-Abelian Ising-like fusion rules.
+
+  The construction is based on first constructing a model for an SPT phase \cite{arxiv:1106.4772,arxiv:1908.02613}, gauging its symmetries following Refs. \cite{arxiv:1202.3120,arxiv:1605.01640,arXiv:1806.08679}, and making all terms commute outside of the ground-state subspace by projecting them to zero flux.
+
+
+features:
+  decoders:
+    - 'Probabilistic local cellular-automaton decoder \cite{arxiv:2405.11719}.'
+
+
+relations:
+  parents:
+    - code_id: commuting_projector
+    - code_id: topological
+      detail: 'Cubic theory codes realize \(\geq 5\)-dimensional higher-form \(\mathbb{Z}_2^3\) gauge theories with non-Abelian excitations.'
+  cousins:
+    - code_id: self_correct
+      detail: 'A family of five-dimensional cubic theory codes with non-Abelian excitations is argued to be self-correcting below a critical temperature via a Peierls argument \cite{arxiv:2405.11719}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-05-23'

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

@@ -7,11 +7,12 @@ code_id: 4d_surface
 physical: qubits
 logical: qubits
 
-name: '4D surface code'
+name: 'Loop toric code'
 introduced: '\cite{arxiv:quant-ph/0110143}'
 
 alternative_names:
   - 'Kitaev tesseract code'
+  - '4D surface code'
 
 description: |
   A generalization of the Kitaev surface code defined on a 4D lattice.
@@ -23,6 +24,8 @@ description: |
 
 
 features:
+  general_gates:
+    - 'Logical \(CZ\), \(S\), and Hadamard gates \cite{arxiv:2405.11719}.'
   code_capacity_threshold:
     - 'Independent \(X,Z\) noise: \(2.117\%\) with Hastings decoder \cite{arxiv:1609.00510} and \(7.3\%\) with RG decoder for 4D surface code \cite{arxiv:1708.09286}.
     It is conjectured via a statistical-mechanical mapping that the optimal ML decoder yields a threshold of \(11.003\%\) \cite{arxiv:hep-th/0310279}.'