refs

codes/quantum/properties/hamiltonian/self_correct.yml

@@ -44,6 +44,7 @@ protection: |
   2D stabilizer codes \cite{arxiv:0810.1983} and encodings of frustration-free code Hamiltonians \cite{arxiv:1209.5750} admit only constant-energy excitations, and so do not have an energy barrier.
   There exist several candidates for self-correction as well as several partially self-correcting memories (see cousins below).
 
+  The lifetime of a ground-state memory protected by a Hamiltonian alone can increase at most logarithmically with \(n\) under depolarizing noise \cite{arxiv:0807.0287,arxiv:0904.4861}, and a clock Hamiltonian can saturate this bound \cite{arxiv:0904.4861}. 
 
 notes:
   - 'Reviews of self-correcting memories \cite{arxiv:1210.3207,arxiv:1411.6643}.'

codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml

@@ -20,7 +20,7 @@ features:
   decoders:
     - 'Renormalization group (RG) decoder \cite{arxiv:1006.1362}.'
     - '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:2211.09803,arxiv:2401.06300,arxiv:2402.14906}; see also Refs. \cite{arxiv:0911.3843,arxiv:1107.3940}.'
+    - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2211.09803,arxiv:2401.06300,arxiv:2402.14906}; see also Refs. \cite{arxiv:0807.0287,arxiv:0911.3843,arxiv:1107.3940}.'
   code_capacity_threshold:
     - 'Noise thresholds can be formulated as anyon \hyperref[topic:code-switching]{condensation} transitions in a topological field theory \cite{arxiv:2301.05687}, generalizing the mapping of the effect of noise on a code state to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}.
     Namely, the noise threshold for a noise channel \(\cal{E}\) acting on a 2D stabilizer state \(|\psi\rangle\) can be obtained from the properties of the resulting (mixed) state \(\mathcal{E}(|\psi\rangle\langle\psi|)\) \cite{arxiv:2301.05238,arxiv:2301.05687,arxiv:2301.05689,arxiv:2309.11879, arxiv:2401.17359}.'

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml

@@ -37,7 +37,7 @@ protection: |
   The joint \(+1\)-eigenspace of the \(Z\)-type Paulis corresponds to the subspace that conserves \(\mathbb{Z}_2\) flux, while the joint \(+1\)-eigenspace of \(X\)-type operators corresponds to the subspace that preserves \(\mathbb{Z}_2\) gauge symmetry (a one-form symmetry).
   Logical Pauli operators correspond to non-contractible Wilson loops in the case of closed boundaries, and to paths connecting different types of boundaries in the case of open boundaries.
 
-  Behavior under Hamiltonian \(X\)-type and \(Z\)-type perturbations is related to an anisotropic 3D gauge Higgs model \cite{arxiv:0804.3175,arxiv:1411.5815}.
+  Behavior under Hamiltonian \(X\)-type and \(Z\)-type perturbations is related to an anisotropic 3D gauge Higgs model \cite{arxiv:cond-mat/0609048,arxiv:0804.3175,arxiv:0807.0487,arxiv:1411.5815}.
   In order to corrupt logical states, any local noise must bring the code state out of the topological order \cite{arxiv:2310.08639}.  
 
   Alternatively, there is a general correspondence between stabilizer codes and gauge theory, with the stabilizer group playing the role of the gauge group \cite{arxiv:2412.15317}.