diff --git a/codes/oaecc.yml b/codes/oaecc.yml index aec6c284f..533d4e928 100644 --- a/codes/oaecc.yml +++ b/codes/oaecc.yml @@ -28,7 +28,7 @@ description: |- \begin{align}\mathcal{A} = \bigoplus_\gamma I_\gamma \otimes \mathcal{L}(\mathsf{B}_\gamma),\end{align} where \(\mathcal{L}(\mathsf{B}_\gamma)\) denotes the full set of linear maps on \(\mathsf{B}_\gamma\). The \(\mathsf{A}_j\) factors can be used to store quantum information, \(\gamma\) indexes the block structure of the code, while \(\mathsf{B}_j\) determine its gauge structure. - Together, the above forms the most general form of an information preserving structure \cite{arxiv:quant-ph/0507213,arxiv:0705.4282,arxiv:1006.1358}. + Together, the above forms the most general form of an information preserving structure \cite{arxiv:quant-ph/0402056,arxiv:quant-ph/0507213,arxiv:0705.4282,arxiv:1006.1358}. protection: | Given an error operation \(\mathcal{E}\), one says that \(\mathcal{A}\) is \textit{correctable} for \(\mathcal{E}\) if there exists a recovery operation \(\mathcal{R}\) such that diff --git a/codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml b/codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml index 8645e03f2..afe432fee 100644 --- a/codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml +++ b/codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml @@ -33,9 +33,6 @@ features: fault_tolerance: - 'Dual-rail qubits can be used to convert leakage and \hyperref[topic:ad]{AD} noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}.' - threshold: - - 'Between \(1.78\%\) and \(11.5\%\) with faulty photon detectors when repeatedly concatenating with the Steane code \cite{arxiv:quant-ph/0502101}.' - realizations: - 'The dual-rail code is ubiquitous in linear-optical quantum devices and is behind the KLM protocol, one of the first proposals for fault-tolerant computation. See reviews \cite{arxiv:quant-ph/0512104,arxiv:quant-ph/0512071,arxiv:1907.06331} for more details.' @@ -55,7 +52,9 @@ relations: detail: 'The two-mode binomial code for \(S=N=0\) reduces to the dual-rail code.' cousins: - code_id: oscillators_concatenated - detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code \cite{doi:10.1038/35051009}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.' + detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code such as the Steane code \cite{doi:10.1038/35051009,arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.' + - code_id: steane + detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code such as the Steane code \cite{doi:10.1038/35051009,arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}.' - code_id: single-mode detail: 'Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code \cite{arxiv:1605.09278}.' - code_id: ampdamp diff --git a/codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml b/codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml index e0dc7c5d0..957622b71 100644 --- a/codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml +++ b/codes/quantum/qubits/small_distance/small/5/stab_5_1_3.yml @@ -53,8 +53,9 @@ features: - 'Pieceable fault-tolerant CZ, CNOT, and CCZ gates \cite{arxiv:1603.03948}.' decoders: - 'Fault-tolerant syndrome extraction circuits \cite{arxiv:quant-ph/9605031,arxiv:quant-ph/9608028}.' - - 'Syndrome extraction circuit using only CNOT-SWAP gates \cite{arxiv:2207.13356}.' + - 'Syndrome extraction circuit optimized for a linear qubit architecture \cite{arxiv:quant-ph/0311116}.' - 'Combined dynamical decoupling and error correction protocol on individually-controlled qubits with always-on Ising couplings \cite{arxiv:1509.01239}.' + - 'Syndrome extraction circuit using only CNOT-SWAP gates \cite{arxiv:2207.13356}.' - 'Symmetric decoder correcting all weight-one Pauli errors. The resulting logical error channel after coherent noise has been explicitly derived \cite{arxiv:2203.01706}.' - 'Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2409.13681}.' diff --git a/codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml b/codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml index b86401c78..c86985fc4 100644 --- a/codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml +++ b/codes/quantum/qubits/stabilizer/hermitian/stabilizer_over_gf4.yml @@ -12,7 +12,7 @@ introduced: '\cite{arxiv:quant-ph/9608006}' alternative_names: - 'Calderbank-Rains-Shor-Sloane (CRSS) code' - - '\(GF(4)\)-linear code' + - '\(GF(4)\)-linear stabilizer code' - '\(M_{3}\) code' # - 'Stabilizer code over \(GF(4)\)' # M3 <-- 1702.06990 diff --git a/codes/quantum/qubits/stabilizer/qldpc/concatenated/concatenated_steane.yml b/codes/quantum/qubits/stabilizer/qldpc/concatenated/concatenated_steane.yml index 46c3ad0f8..7c7ebcfea 100644 --- a/codes/quantum/qubits/stabilizer/qldpc/concatenated/concatenated_steane.yml +++ b/codes/quantum/qubits/stabilizer/qldpc/concatenated/concatenated_steane.yml @@ -27,6 +27,7 @@ features: code_capacity_threshold: - 'This family is one of the first to admit a \hyperref[topic:computational-threshold]{concatenated threshold} \cite{arxiv:quant-ph/9702058,arxiv:quant-ph/9809054,arxiv:quant-ph/0207119,arxiv:quant-ph/0410047,arxiv:quant-ph/0504218,arxiv:quant-ph/0703230,arxiv:quant-ph/0604090}; see the book \cite{preset:GottesmanBook}.' threshold: + - 'Between \(1.78\%\) and \(11.5\%\) with faulty photon detectors when combined with the dual-rail code at the first concatenation step in a variant of the KLM protocol \cite{arxiv:/quant-ph/0405112,arxiv:quant-ph/0502101}.' - 'Numerical study of \hyperref[topic:computational-threshold]{concatenated thresholds} of logical CNOT gates for various codes against depolarizing noise \cite{arxiv:0711.1556}; see also \cite{arxiv:quant-ph/0406025}.' - 'A \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.' diff --git a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml index 5b14b816d..e88a1c577 100644 --- a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml +++ b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml @@ -12,6 +12,7 @@ introduced: '\cite{arxiv:quant-ph/9605005,arxiv:quant-ph/9705052}' alternative_names: - 'Pauli stabilizer code' + - 'Symplectic code' - 'Additive quantum code' - 'Additive CWS code' - 'Clifford code' @@ -81,7 +82,7 @@ description: | The sets of \(GF(4)\)-represented vectors for all generators yield a trace-Hermitian self-orthogonal additive quaternary code. This classical code corresponds to the stabilizer group \(\mathsf{S}\) while its trace-Hermitian dual corresponds to the normalizer \(\mathsf{N(S)}\). In the case of stabilizer states, the correspondence is between such states and trace-Hermitian self-dual quaternary codes; such codes, and therefore such states, have been classified up to equivalence for \(n \leq 12\) \cite{arxiv:quant-ph/0503236,arxiv:math/0504522}. - There is a complete set of invariants characterizing stabilizer states up to equivalence \cite{arxiv:quant-ph/0410165}. + There is a complete set of invariants characterizing stabilizer states up to equivalence \cite{arxiv:quant-ph/0410165,arxiv:quant-ph/0404106}. ZX calculus is complete, sound, and universal for qubit stabilizer codes \cite{arxiv:1307.7025}. Any stabilizer code can be represented by a \textit{ZX canonical form} (ZXCF) \cite{arxiv:2411.14448}, and there exist two other representations \cite{arxiv:2205.02009,arxiv:2411.14448} that utilize ZX calculus. @@ -173,6 +174,7 @@ features: - 'Greedy syndrome measurement schedule \cite{arxiv:2409.14283}.' - 'Dynamical weight reduction (DWR) scheme in which measurements of smaller-weight Paulis yield the outcome of a larger-weight Pauli via the use of ZX calculus and ancillary qubits \cite{arxiv:2410.12527}.' - 'Ancilla modes can be used for syndrome extraction instead of ancilla qubits \cite{arxiv:quant-ph/0511098}, and using two-component cat codes \cite{arxiv:1807.09334} yields fault-tolerant syndrome extraction circuits.' + - 'Continuous-time QEC protocol \cite{arxiv:quant-ph/0402017}.' - '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}.' @@ -219,7 +221,7 @@ notes: - 'Introductions to stabilizer codes can be found in \cite{arxiv:quant-ph/9705052,preset:PreskillNotes,doi:10.1002/9783527618637.ch1}.' - 'Tables of bounds and examples of stabilizer codes for various \(n\) and \(k\), based on algorithms developed in Ref. \cite{doi:10.1007/978-3-540-37634-7_13}, are maintained by M. Grassl at this \href{https://codetables.markus-grassl.de/}{website}. A Magma implementation exists at this \href{https://magma.maths.usyd.edu.au/magma/handbook/text/1976}{website}.' - 'See Quantum Codes qubit stabilizer database, maintained by N. Aydin, P. Liu, and B. Yoshino \cite{arxiv:2106.12065,arxiv:2108.03567}, at this \href{https://quantumcodes.info/}{website}.' - - 'Entanglement purification protocols with qubit stabilizer codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0209091}. There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}.' + - 'Entanglement purification protocols with qubit stabilizer codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0209091}. There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}. Purification protocols using two-way classical channels can exceed the quantum Hamming and quantum Singleton bounds \cite{arxiv:quant-ph/0310097}.' - 'The overlap between any stabilizer codeword and any \(n\)-qubit product state is at most \(2/2^d\) \cite[Thm. 2]{arxiv:2405.01332}.' - 'Qubit stabilizer codes can be used to estimate physical Pauli noise up to their \hyperref[topic:quantum-weight-enumerator]{pure distance} \cite{arxiv:2107.14252}, and logical Pauli noise for any correctable physical noise \cite{arxiv:2209.09267}.' - 'The stabilizer formalism has been gamified \cite{arxiv:2405.06795}.' diff --git a/codes/quantum/qudits/stabilizer/qudit_css.yml b/codes/quantum/qudits/stabilizer/qudit_css.yml index 0c8ff1a08..70cf36c8f 100644 --- a/codes/quantum/qudits/stabilizer/qudit_css.yml +++ b/codes/quantum/qudits/stabilizer/qudit_css.yml @@ -8,7 +8,7 @@ physical: qudits logical: qudits name: 'Modular-qudit CSS code' -introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029}' +introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9703048}' description: | An \(((n,K,d))_q\) modular-qudit stabilizer code admitting a set of stabilizer generators that diff --git a/codes/quantum/qudits_galois/stabilizer/css/galois_css.yml b/codes/quantum/qudits_galois/stabilizer/css/galois_css.yml index 8afa5fb95..4450877cc 100644 --- a/codes/quantum/qudits_galois/stabilizer/css/galois_css.yml +++ b/codes/quantum/qudits_galois/stabilizer/css/galois_css.yml @@ -8,7 +8,7 @@ physical: galois logical: galois name: 'Galois-qudit CSS code' -introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9608049,arxiv:quant-ph/9703048,arxiv:quant-ph/9911011,arxiv:quant-ph/0312164,doi:10.1016/j.disc.2007.08.038}' +introduced: '\cite{arxiv:quant-ph/9512032,doi:10.1103/PhysRevLett.77.793,arxiv:quant-ph/9601029,arxiv:quant-ph/9608049,arxiv:quant-ph/9911011,arxiv:quant-ph/0312164,doi:10.1016/j.disc.2007.08.038}' alternative_names: - 'Euclidean code' diff --git a/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml b/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml index 3bcd7b7f3..2acd2810d 100644 --- a/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml +++ b/codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml @@ -11,7 +11,7 @@ name: 'Hermitian Galois-qudit code' introduced: '\cite[Corr. 5]{arxiv:quant-ph/9703048}\cite{doi:10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T,doi:10.1109/18.959288,arxiv:quant-ph/0508070}' alternative_names: - - '\(GF(q^2)\)-linear code' + - '\(GF(q^2)\)-linear stabilizer code' # - 'Stabilizer code over \(GF(q^2)\)' description: |