diff --git a/codes/quantum/properties/block/single_shot.yml b/codes/quantum/properties/block/single_shot.yml index e59d72277..a05ddf634 100644 --- a/codes/quantum/properties/block/single_shot.yml +++ b/codes/quantum/properties/block/single_shot.yml @@ -6,16 +6,23 @@ code_id: single_shot name: 'Single-shot code' -introduced: \cite{arxiv:1404.5504} +introduced: \cite{arxiv:1404.5504,arxiv:1805.09271} description: | Measurement errors during decoding can yield the wrong syndrome outcome, which can cause error correction to fail even against correctable data errors. A single-shot code is a block quantum code admitting a fault-tolerant error-correcting protocol that does not "fail too badly" when faced with noisy syndrome measurements. + The property typically implies that a sufficiently large number of error-correction rounds will keep both data and measurement errors bounded, as opposed to causing to eventually become uncorrectable. + The property is sufficient (but not necessary \cite{arxiv:2002.05180}) to reduce the number of error-correction rounds required for fault-tolerant error correction. + In the loosest form of the single-shot property for qubit, modular qudit, or Galois qudit codes, given some data error \(e\), ideal data error syndrome \(s\), and measurement error \(m\), there exists an error-correction protocol that outputs a correction \(f\) such that the Hamming weight of the residual error after correction, \(e+f\), is \textit{polynomial} in the weight of \(m\). Note that the \textit{stabilizer-reduced weight} \cite{arxiv:1805.09271} of \(e\) is often used instead of the weight of \(e\), with the justification that many decoders are desgined to obtain the minimum-weight error representative. - The single-shot property usually implies that a sufficiently large number of error-correction rounds will keep both data and measurement errors bounded, as opposed to causing to eventually become uncorrectable. + Typical noise models considered include stochastic noise \cite{arxiv:1404.5504} and adversarial noise \cite{arxiv:1805.09271}. + +# This can happen for some QLDPC codes and some abelian topological codes. +# The property is named after its primary implication, namely, that one can obtain fault-tolerant syndrome data from only a single round of error correction. + # In other words, the single-shot property implies that the number of error-correcting rounds necessary for successful error correction is independent of the number of subsystems \(n\). diff --git a/codes/quantum/qubits/stabilizer/qldpc/homological/quantum_expander.yml b/codes/quantum/qubits/stabilizer/qldpc/homological/quantum_expander.yml index bc922b59f..2c1b45eaf 100644 --- a/codes/quantum/qubits/stabilizer/qldpc/homological/quantum_expander.yml +++ b/codes/quantum/qubits/stabilizer/qldpc/homological/quantum_expander.yml @@ -32,6 +32,8 @@ features: relations: parents: - code_id: hypergraph_product + - code_id: single_shot + detail: 'Quantum expander codes are single-shot \cite{arxiv:1808.03821}.' cousins: - code_id: expander # detail: 'Quantum expander codes are constructed from classical expander codes.' diff --git a/codes/quantum/qubits/stabilizer/qubit_css.yml b/codes/quantum/qubits/stabilizer/qubit_css.yml index 88a2c594e..240af4533 100644 --- a/codes/quantum/qubits/stabilizer/qubit_css.yml +++ b/codes/quantum/qubits/stabilizer/qubit_css.yml @@ -104,6 +104,7 @@ features: - 'Homomorphic gadgets fault-tolerant measurement unify Steane and Shor error correction \cite{arxiv:2211.03625}.' - 'Parallel syndrome extraction for distance-three codes can be done fault-tolerantly using one flag qubit \cite{arXiv:2208.00581}.' - 'Distance-preserving flag fault-tolerant error correction using lookup tables for small codes \cite{arxiv:2306.12862}.' + - 'A fault-tolerant error-correction protocol using \(O(d\log d)\) syndrome measurements can be applied to any CSS code with distance \(d \geq \Omega(n^{\alpha})\) for any \(\alpha > 0\) \cite{arxiv:2002.05180}.' code_capacity_threshold: - 'Bounds on code capacity thresholds for various noise models exist in terms of stabilizer generator weights \cite{arxiv:1208.2317,arxiv:1412.6172}.' decoders: @@ -144,6 +145,9 @@ relations: - code_id: ag detail: 'Algebraic geometry codes can be plugged into the CSS construction to yield asymptotically good quantum codes \cite{arxiv:quant-ph/0006061}.' +# - code_id: single_shot +# detail: 'A fault-tolerant error-correction protocol using \(O(d\log d)\) syndrome measurements can be applied to any CSS code with distance \(d \geq \Omega(n^{\alpha})\) for any \(\alpha > 0\) \cite{arxiv:2002.05180}. This implies that the single-shot property is not necessary to reduce the number of error-correction rounds required for fault tolerance.' + # Begin Entry Meta Information _meta: diff --git a/codes/quantum/qubits/stabilizer/topological/color.yml b/codes/quantum/qubits/stabilizer/topological/color.yml index 53dc80726..dea76694c 100644 --- a/codes/quantum/qubits/stabilizer/topological/color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color.yml @@ -49,7 +49,6 @@ features: - '\(\geq 6.25\%\) threshold for 2D color codes with error-free syndrome extraction, and \(0.1\%\) with faulty syndrome extraction \cite{arXiv:0907.1708}.' - '\(0.46\%\) for 3D codes with clustering decoder \cite{arXiv:1708.07131}.' - '\(1.9\%\) for 1D string-like logical operators and \(27.6\%\) for 2D sheet-like operators for 3D codes with noise models using optimal decoding and perfect measurements \cite{arXiv:1708.07131}.' - - '\(0.31\%\) noise threshold error rate for gauge code using clustering decoder \cite{arXiv:1503.08217}.' - '\(0.2\%\) with depolarizing circuit-level noise using two flag-qubits per stabilizer generator and the restriction decoder \cite{arXiv:1911.00355}.' - '\(0.143\%\) with depolarizing circuit-level noise using perfect-matching decoder \cite{arXiv:1407.5103}.' - '\(>0\%\) threshold with sweep decoder \cite{doi:10.7907/059V-MG69}.' diff --git a/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml b/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml index c6c0effda..6ac28ceec 100644 --- a/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml +++ b/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml @@ -18,7 +18,7 @@ relations: parents: - code_id: subsystem_stabilizer - code_id: single_shot - detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621}.' + detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621,arxiv:2305.06365}.' cousins: - code_id: 3d_surface - code_id: self_correct diff --git a/codes/quantum/qubits/subsystem/topological/subsystem_color.yml b/codes/quantum/qubits/subsystem/topological/subsystem_color.yml index f499f885d..442fbade9 100644 --- a/codes/quantum/qubits/subsystem/topological/subsystem_color.yml +++ b/codes/quantum/qubits/subsystem/topological/subsystem_color.yml @@ -10,17 +10,27 @@ logical: qubits name: 'Subsystem color code' introduced: '\cite{arxiv:0908.4246,arxiv:1311.0879}' +alternative_names: + - 'Gauge color code' + description: | Stub. +features: + decoders: + - '\(0.31\%\) noise threshold error rate using clustering decoder \cite{arXiv:1503.08217}.' + + relations: parents: - code_id: subsystem_stabilizer + - code_id: single_shot + detail: 'The subsystem color code is a single-shot code \cite{arxiv:1503.08217}.' cousins: - code_id: color - code_id: symmetry_protected_self_correct detail: 'A particular gauge-fixed version of this code on a 3D lattice yields a self-correcting memory protected by one-form symmetries (see Sec. IV D of Ref. \cite{arXiv:1805.01474}). The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length. - The gauge color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.' + The subsystem color code is not a self-correcting quantum memory if symmetry protection is removed \cite{arxiv:2305.06389}.' # Begin Entry Meta Information