refs

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -95,6 +95,7 @@ features:
     There exist various performance metrics for magic-state distillation \cite{arxiv:quant-ph/9806094,arxiv:1807.10296,arxiv:1901.03322,arxiv:1904.01124}.
     The Hadamard gate cannot be obtained from a magic state \cite{arxiv:2312.03515}.'
     - 'Logical circuit synthesis (LCS) taking in a code and a logical Clifford operation and producing a circuit acting on the physical qubits \cite{arxiv:1907.00310}.'
+    - 'Clifford stabilizer circuits can be compiled using tableaux manipulation \cite{arxiv:2404.19408}.'
   decoders:
     - 'The structure of stabilizer codes allows for \textit{syndrome-based decoding}, where errors are corrected based on the results of stabilizer measurements (\textit{syndromes}). The size of the circuit extracting the syndrome depends on the weight of its corresponding stabilizer generator.'
     - 'MPE decoding, i.e., the process of finding the most likely error, is \(NP\)-complete in general \cite{arxiv:1009.1319,manual:{Kuo, Kao-Yueh, and Chung-Chin Lu. "On the hardness of decoding quantum stabilizer codes under the depolarizing channel." 2012 International Symposium on Information Theory and its Applications. IEEE, 2012.}}. If the noise model is such that the most likely error is the lowest-weight error, then ML decoding is called \textit{minimum-weight} decoding. Maximum-likelihood (ML) decoding (a.k.a.\ degenerate maximum-likelihood decoding), i.e., the process of finding the most likely error class (up to degeneracy of errors), is \(\#P\)-complete in general \cite{arxiv:1310.3235}.'

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

@@ -119,7 +119,7 @@ features:
     ML decoding \cite{arxiv:quant-ph/0110143} is \(\#P\)-hard in general for the surface code \cite{arxiv:2309.10331}.'
     - 'Union-find decoder \cite{arxiv:1709.06218} uses the \textit{union-find data structure} \cite{doi:10.1145/364099.364331,doi:10.1137/0202024,doi:10.1145/62.2160}, solving the MPE decoding problem exactly for low-weight errors under depolarizing noise. A subsequent modification utilizes the continuous signal obtained in the physical implementation of the stabilizer measurement (as opposed to discretizing the signal into a syndrome bit) \cite{arxiv:2107.13589}. Belief union find is a combination of belief-propagation and union-find \cite{arxiv:2203.04948}.
     Strictly local (as opposed to partially local) union find \cite{arxiv:2305.18534} has a worst-case runtime of order \(O(d^3)\) in the distance \(d\).'
-    - 'Modified MWPM decoders: pipeline MWPM (accounting for correlations between events) \cite{arxiv:1310.0863,arxiv:2205.09828}; modification tailored to asymmetric noise \cite{arxiv:1812.01505}; parity blossom MWPM and fusion blossom MWPM \cite{arxiv:2305.08307}, a modification utilizing the continuous signal obtained in the physical implementation of the stabilizer measurement (as opposed to discretizing the signal into a syndrome bit) \cite{arxiv:2107.13589}; belief perfect matching (a combination of belief-propagation and MWPM) \cite{arxiv:2203.04948}.
+    - 'Modified MWPM decoders: pipeline MWPM (accounting for correlations between events) \cite{arxiv:1310.0863,arxiv:2205.09828}; modification tailored to asymmetric noise \cite{arxiv:1812.01505}; parity blossom MWPM and fusion blossom MWPM \cite{arxiv:2305.08307}, a modification utilizing the continuous signal obtained in the physical implementation of the stabilizer measurement (as opposed to discretizing the signal into a syndrome bit) \cite{arxiv:2107.13589}; belief perfect matching (a combination of belief-propagation and MWPM) \cite{arxiv:2203.04948}; and spanning tree matching (STM) and rapid-fire (RFire) decoders \cite{arxiv:2405.01151}.
     Combinining, or \textit{harmonizing}, various decoders can improve performance \cite{arxiv:2401.12434}.'
     - 'Renormalization group (RG) \cite{arxiv:0911.0581,arxiv:1304.6100,arxiv:1411.3028}; see Ref. \cite{arxiv:1310.2393} for the planar surface code.'
     - 'Linear-time ML erasure decoder \cite{arxiv:1703.01517}.'