From 78e9d385ce9586a6184d1c79687eb51bf107682f Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Wed, 25 Sep 2024 17:25:58 -0400 Subject: [PATCH] refs --- codes/classical/analog/analog.yml | 3 +++ codes/quantum/qubits/stabilizer/css/quantum_parity.yml | 2 +- codes/quantum/qubits/stabilizer/qubit_stabilizer.yml | 2 ++ .../qubits/stabilizer/topological/color/hyperbolic_color.yml | 2 ++ .../surface/2d_surface/rotated_surface/rotated_surface.yml | 2 +- .../surface/2d_surface/two_dimensional_hyperbolic_surface.yml | 1 + 6 files changed, 10 insertions(+), 2 deletions(-) diff --git a/codes/classical/analog/analog.yml b/codes/classical/analog/analog.yml index 1495482b0..7881a7f18 100644 --- a/codes/classical/analog/analog.yml +++ b/codes/classical/analog/analog.yml @@ -77,6 +77,9 @@ relations: - code_id: block - code_id: group_classical detail: 'Sphere-packing alphabets \(\mathbb{R}^n\) are infinite fields, which are groups under addition.' + cousins: + - code_id: hamiltonian + detail: 'The Cohn-Elkies linear programming bound is related to the conformal bootstrap, which is a way of utilizing symmetry to constrain correlation functions of conformal field theories \cite{arxiv:1905.01319}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/stabilizer/css/quantum_parity.yml b/codes/quantum/qubits/stabilizer/css/quantum_parity.yml index e4eb8195c..3577c1a85 100644 --- a/codes/quantum/qubits/stabilizer/css/quantum_parity.yml +++ b/codes/quantum/qubits/stabilizer/css/quantum_parity.yml @@ -42,7 +42,7 @@ protection: 'Has distance \(d=\min(m_1,m_2)\).' features: encoders: - - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294} and tree tensor networks \cite{arxiv:1312.4578}.' + - 'Encoders for a recursively concatenated QPCs are related to \textit{quantum trees} \cite{arxiv:2305.03694,arxiv:2306.14294,arxiv:2409.13801} and tree tensor networks \cite{arxiv:1312.4578}.' - 'Linear-optical encoding \cite{arxiv:0707.0903}.' decoders: - 'Teleportation-based QEC \cite{arxiv:1310.5291}.' diff --git a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml index 10a91ed59..b3814eeda 100644 --- a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml +++ b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml @@ -129,6 +129,7 @@ features: decoders: - 'The size of the circuit extracting the syndrome depends on the weight of its corresponding stabilizer generator. Syndrome extraction circuits can be simulated efficiently using dedicated software (e.g., STIM \cite{arxiv:2103.02202}) and there are many general schemes for generating them \cite{arxiv:2408.01339} (see also \cite{arxiv:2402.04093}).' - 'DiVincenzo-Aliferis syndrome extraction circuits \cite{arxiv:quant-ph/0607047}.' + - 'Greedy syndrome measurement schedule \cite{arxiv:2409.14283}.' - '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}.' - 'Incorporating faulty syndrome measurements can be done by performing spacetime decoding, i.e., using data from past rounds for decoding syndromes in any given round. If a decoder does not process syndrome data sufficiently quickly, it can lead to the \textit{backlog problem} \cite{arxiv:1302.3428}, slowing down the computation.' - 'Splitting decoders \cite{arxiv:2309.15354}.' @@ -157,6 +158,7 @@ features: - 'Fault-tolerant constant-depth unencoder transforming logical states into physical states using single-qubit measurements \cite{arxiv:2408.06299}.' - 'Post-selection based algorithm preparing magic state corresponding to arbitrary rotations \cite{arxiv:2303.17380}.' - '\hyperref[topic:code-switching]{Code switching} can be done using only transversal gates for qubit stabilizer codes \cite{arxiv:2409.13465}.' + - 'Flag-Proxy Networks (FPNs) \cite{arxiv:2409.14283}.' code_capacity_threshold: - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}. The AQEC relative entropy is related to the resulting threshold \cite{arxiv:2312.16991}.' diff --git a/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml b/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml index b6651e86b..616bd8cf5 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml @@ -25,6 +25,8 @@ protection: | features: rate: 'In the double-cover construction \cite{arxiv:1301.6588}, an \(\{\ell,m\}\) input tiling yields a code family with an asymptotic rate of \(1 - 1/\ell - 1/m\).' + decoders: + - 'Two flag-based decoders \cite{arxiv:2409.14283}.' relations: diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/rotated_surface/rotated_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/rotated_surface/rotated_surface.yml index 278ff6754..e27886b52 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/rotated_surface/rotated_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/rotated_surface/rotated_surface.yml @@ -44,7 +44,7 @@ features: relations: parents: - code_id: surface - detail: 'The lattice of the rotated surface code can be obtained by taking the medial graph of the surface code lattice (treated as a graph) and applying a similar procedure to construct the check operators \cite{arxiv:quant-ph/0703272,arxiv:1606.07116}\cite[Fig. 8]{arxiv:2101.09349}. Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}.' + detail: 'The lattice of the rotated surface code can be obtained by taking the medial graph of the surface code lattice (treated as a graph) and applying a similar procedure to construct the check operators \cite{arxiv:quant-ph/0703272,arxiv:1606.07116}\cite[Fig. 8]{arxiv:2101.09349}. Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}. The rotated surface code presents certain savings over the original surface code \cite{arxiv:2409.14765}.' - code_id: quantum_tanner detail: 'Applying the quantum Tanner transformation to the surface code yields the rotated surface code \cite{manual:{Nikolas P. Breuckmann, private communication, 2022},manual:{Anthony Leverrier, \href{https://github.com/errorcorrectionzoo/eczoo_data/files/9210173/rotated.pdf}{Mapping the toric code to the rotated toric code}, 2022.}}.' - code_id: hierarchical diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/two_dimensional_hyperbolic_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/two_dimensional_hyperbolic_surface.yml index 58387ab83..8cba709ca 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/two_dimensional_hyperbolic_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/two_dimensional_hyperbolic_surface.yml @@ -31,6 +31,7 @@ features: decoders: - 'Due to the symmetries of hyperbolic surface codes, optimal measurement schedules of the stabilizers can be found \cite{arxiv:2010.09626}.' - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:1804.01950}.' + - 'Two flag-based decoders \cite{arxiv:2409.14283}.' code_capacity_threshold: - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:1805.00644}.'