topological stability refs

errorcorrectionzoo · May 21, 2024 · 8c88e9d · 8c88e9d
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diff --git a/codes/quantum/properties/block/topological/topological.yml b/codes/quantum/properties/block/topological/topological.yml
@@ -53,6 +53,10 @@ description: |
 # Frohlich braiding anyons doi:10.1142/S0129055X90000107,
 # Mention [39-41] in arxiv:2211.03798
 
+protection: |
+  Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds form a large class of topological phases.
+  They satisfy the topological order (TO) conditions \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.
+
 features:
   rate: 'The logical dimension \(K\) of 2D topological codes described by unitary modular fusion categories depends on the type of manifold \(\Sigma^2\) that is tesselated to form the many-body system.
   For closed orientable manifolds \cite{doi:10.1007/bf01217730,doi:10.1007/BF01238857},

diff --git a/codes/quantum/properties/hamiltonian/commuting_projector.yml b/codes/quantum/properties/hamiltonian/commuting_projector.yml
@@ -11,12 +11,18 @@ name: 'Commuting-projector code'
 description: |
   Hamiltonian-based code whose Hamiltonian terms can be expressed as orthogonal projectors (i.e., Hermitian operators with eigenvalues 0 or 1) that commute with each other.
 
+protection: |
+  Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the TO conditions, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.
+
 
 
 
 relations:
   parents:
     - code_id: hamiltonian
+  cousins:
+    - code_id: topological
+      detail: 'Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the TO conditions, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml b/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml
@@ -66,9 +66,6 @@ relations:
       detail: 'Lattice stabilizer codes are QLDPC codes on Euclidean geometries.'
     - code_id: quantum_quasi_cyclic
       detail: 'Lattice stabilizer codes are invariant under translations by a lattice unit cell.'
-  cousins:
-    - code_id: hamiltonian
-      detail: 'Lattice stabilizer code Hamiltonians are stable with respect to small perturbations \cite{arxiv:1001.4363,arxiv:1001.0344}, meaning that the notion of a phase can be defined.'
 
 
 

diff --git a/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml b/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml
@@ -96,7 +96,8 @@ relations:
       detail: 'A compass code on a fully non-colored lattice reduces to the Bacon-Shor code.'
   cousins:
     - code_id: hamiltonian
-      detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.'
+      detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.
+      Bacon-Show code Hamiltonians can be used to suppress errors in adiabatic quantum computation \cite{arxiv:1511.01997}, while subspace-code two-local Hamiltonians cannot \cite{arxiv:1410.5487}.'
     - code_id: floquet
       detail: 'The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule \cite{arxiv:2403.03291}.'