refs

codes/quantum/groups/topological/quantum_double_dihedral.yml

@@ -20,6 +20,9 @@ features:
   general_gates:
     - 'Universal topological quantum computation is possible for certain groups such as \(G=D_3=S_3\) \cite{arxiv:quant-ph/0306063,arxiv:0901.1345}.'
     - '\(U\)-model gate set \cite{arxiv:1401.7096}, which can protect from circuit-level noise with the help of an anyon interferometer for the case of \(G=S_3\) \cite{arxiv:2411.09697}.'
+  code_capacity_threshold:
+    - 'The threshold under ML decoding for the \(G=D_4\) quantum double corresponds to the value of a critical point of a disordered \(D_4\) rotor model \cite{arxiv:2409.12230,arxiv:2409.12948}.'
+
   fault_tolerance:
     - 'Universal topological quantum computation is possible for certain groups such as \(G=D_3=S_3\) \cite{arxiv:quant-ph/0306063,arxiv:0901.1345}.'
     - '\(U\)-model gate set \cite{arxiv:1401.7096}, which can protect from circuit-level noise with the help of an anyon interferometer for the case of \(G=S_3\) \cite{arxiv:2411.09697}.'

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

@@ -59,7 +59,8 @@ description: |
   There exist functions of code states that extract the total quantum dimension \(D\) \cite{arxiv:hep-th/0510092,arxiv:cond-mat/0510613}, the topological \(S\)-matrix \cite{arxiv:1111.2342,arxiv:1407.2926}, and the chiral central charge \(c_-\) \cite{arxiv:2110.06932}.
   No observable can distinguish topological order from product states \cite[Appx. I]{arxiv:2106.12627}.
 
-  There is no 2D bosonic topological order at nonzero temperature \cite{arxiv:1106.6026}.
+  There is no 1D bosonic topological order at nonzero temperature \cite{arxiv:1804.05457}, and no commuting-projector model with nontrivial 2D topological order at nonzero temperature \cite{arxiv:1106.6026}. 
+  General thermal states are separable above a sufficiently high temperature \cite{arxiv:2403.16850}.
 
   \subsection{3D and higher-dimensional topological codes}
 

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

@@ -48,7 +48,7 @@ features:
 
   code_capacity_threshold:
     - 'Independent \(X,Z\) noise: \(p_X = 10.31\%\) under MWPM decoding \cite{arxiv:quant-ph/0207088} (see also Ref. \cite{arxiv:1405.4883}), \(9.9\%\) under BP-OSD decoding \cite{arxiv:2005.07016}, and \(8.9\%\) under GBP decoding \cite{arxiv:2212.03214}.
-    The threshold under ML decoding corresponds to the value of a critical point of the two-dimensional random-bond Ising model (RBIM) on the Nishimori line \cite{doi:10.1143/JPSJ.55.3305,arxiv:quant-ph/0110143}, calculated to be \(10.94 \pm 0.02\%\) in Ref. \cite{arxiv:cond-mat/0010143}, \(10.93(2)\%\) in Ref. \cite{arxiv:cond-mat/0106023}, \(10.9187\%\) in Ref. \cite{arxiv:0811.0464}, \(10.917(3)\%\) in Ref. \cite{arxiv:0811.2101}, \(10.939(6)\%\) in Ref. \cite{arxiv:0902.4153}, and estimated to be between \(10.9\%\) and \(11\%\) in Ref. \cite{arxiv:1405.4883}.
+    The threshold under ML decoding corresponds to the value of a critical point of a two-dimensional random-bond Ising model (RBIM) on the Nishimori line \cite{doi:10.1143/JPSJ.55.3305,arxiv:quant-ph/0110143}, calculated to be \(10.94 \pm 0.02\%\) in Ref. \cite{arxiv:cond-mat/0010143}, \(10.93(2)\%\) in Ref. \cite{arxiv:cond-mat/0106023}, \(10.9187\%\) in Ref. \cite{arxiv:0811.0464}, \(10.917(3)\%\) in Ref. \cite{arxiv:0811.2101}, \(10.939(6)\%\) in Ref. \cite{arxiv:0902.4153}, and estimated to be between \(10.9\%\) and \(11\%\) in Ref. \cite{arxiv:1405.4883}.
     Above values are for one type of noise only, and the ML threshold for combined \(X\) and \(Z\) noise is \(2p_X - p_X^2 \approx 20.6\%\).'
     - 'Depolarizing noise: between \(17\%\) and \(18.5\%\) under BSV tensor-network decoding \cite{arxiv:1405.4883}, \(14\%\) under GBP decoding \cite{arxiv:2212.03214}, \(16.5\%\) under recursive MWPM \cite{arxiv:2212.11632}, between \(16\%\) and \(17.5\%\) under AMBP4 (depending on whether surface or toric code is considered) \cite{arxiv:2104.13659}, and between \(15\%\) and \(16\%\) under RG \cite{arxiv:0911.0581}, Markov-chain \cite{arxiv:1302.2669}, or MWPM \cite{arxiv:0905.0531} decoding.
     The threshold under ML decoding corresponds to the value of a critical point of the disordered eight-vertex Ising model, calculated to be \(18.9(3)\%\) \cite{arxiv:1202.1852} (see also APS Physics viewpoint \cite{doi:10.1103/Physics.5.50}).'
@@ -60,6 +60,7 @@ features:
     - 'Coherent noise: the threshold under ML decoding corresponds to the value of a critical point of a particular random-bond Ising model (RBIM) called the complex-coupled Ashkin-Teller model \cite{arxiv:2410.22436,arxiv:2411.05785}.'
 
   threshold:
+    - 'The threshold under ML decoding with measurement errors corresponds to the value of a critical point of a three-dimensional random plaquette model \cite{arxiv:quant-ph/0110143,arxiv:quant-ph/0207088}.'
     - '\(0.133\%\) for independent \(X,Z\) noise and faulty syndrome measurements using a cellular automaton decoder \cite{arxiv:1609.00510}.'
 
 realizations:

codes/quantum/qubits/stabilizer/topological/surface/higher_dimensional_surface.yml

@@ -51,7 +51,7 @@ features:
     - 'Locality preserving operations can be determined for stacks of homoogical codes in any dimension \cite{arxiv:1709.00020}.'
 
   decoders:
-    - 'Sweep decoder \cite{doi:10.7907/059V-MG69}.'
+    - 'Sweep decoder \cite{arxiv:1809.10145,doi:10.7907/059V-MG69}.'
     - 'Improved BP-OSD decoder \cite{arxiv:2206.03122}.'
     - 'Renormalization group (RG) decoder \cite{arxiv:1708.09286}.'
   code_capacity_threshold: