diff --git a/codes/quantum/qubits/dynamic/floquet/honeycomb.yml b/codes/quantum/qubits/dynamic/floquet/honeycomb.yml index ecb328faa..2c8b5d984 100644 --- a/codes/quantum/qubits/dynamic/floquet/honeycomb.yml +++ b/codes/quantum/qubits/dynamic/floquet/honeycomb.yml @@ -56,11 +56,11 @@ relations: - code_id: qudit_znone detail: 'The dynamically generated logical qubit of the honeycomb Floquet code is generated by appropriately scheduling measurements of the gauge generators of the \(\mathbb{Z}_{q=2}^{(1)}\) subsystem stabilizer code corresponding to the Kitaev honeycomb model. However, since this subsystem code has zero logical qubits, the instantaneous stabilizer codes of the honeycomb code cannot be interpreted as gauge-fixed versions of this subsystem code.' - code_id: surface - detail: 'Measurement of each check operator of the honeycomb Floquet code involves two qubits and projects the state of the two qubits to a two-dimensional subspace, which we regard as an effective qubit. + detail: 'Measurement of each check operator of the honeycomb Floquet code involves two qubits and projects the state of the two qubits to a two-dimensional subspace, which we regard as an effective qubit. These effective qubits form a surface code on a hexagonal superlattice. Electric and magnetic operators on the embedded surface code correspond to outer logical operators of the Floquet code. In fact, outer logical operators transition back and forth from magnetic to electric surface code operators under the measurement dynamics. - Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}. + Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR. Numerical comparisons have been performed \cite{arxiv:2410.07065}.' - code_id: twist_defect_surface detail: 'Fermionic string excitations of the honeycomb Floquet code can be condensed along one-dimensional paths, yielding twist defects \cite{arxiv:2306.08027}.' diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index e56ed032e..c11914301 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -117,7 +117,7 @@ features: Decompositions in terms of Toffoli and Hadamard gates \cite{arxiv:quant-ph/0205115} as well as cosine-sine gates also exist \cite{arxiv:quant-ph/0404089}. Gate errors in circuit synthesis can sometimes add up destructively \cite{arxiv:1612.01011}.' - '\begin{defterm}{Clifford hierarchy} \label{topic:clifford-hierarchy} - The Clifford hierarchy \cite{arxiv:quant-ph/9908010,arxiv:1608.06596,arxiv:1902.04022,arXiv:2212.05398} is a tower of gate sets which includes Pauli and Clifford gates at its first two levels, and non-Clifford gates at higher levels. + The Clifford hierarchy \cite{arxiv:quant-ph/9908010,arxiv:1608.06596,arxiv:1902.04022,arXiv:2212.05398,arxiv:2410.11818} is a tower of gate sets which includes Pauli and Clifford gates at its first two levels, and non-Clifford gates at higher levels. The \(k\)th level is defined recursively by \begin{align} C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~, diff --git a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml index 608e3a938..79b154e17 100644 --- a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml +++ b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml @@ -136,6 +136,7 @@ features: - '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}.' + - '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}.' - '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}.' diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml index 43d46d644..1022d7e08 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml @@ -88,7 +88,7 @@ relations: Conversely, the 2D color code can \hyperref[topic:code-switching]{condense} to form the 2D surface code in nine different ways, i.e., by adding two body hopping terms along one of its three triangular directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}. Both the surface and 2D color codes can be constructed from two distinct types of lattices, namely, 4-valent and 3-valent 3-colorable lattices, respectively \cite{arxiv:1107.3502}.' - code_id: 3d_color - detail: 'Gauge fixing can be used to switch between 2D and 3D color codes, thereby yielding fault-tolerant computation with constant time overhead using only local quantum operations \cite{arxiv:1412.5079}.' + detail: 'Gauge fixing can be used to \hyperref[topic:code-switching]{code switch} between 2D and 3D color codes, thereby yielding fault-tolerant computation with constant time overhead using only local quantum operations \cite{arxiv:1412.5079}. There is a fault-tolerant measurement-free scheme for \hyperref[topic:code-switching]{code switching} between 2D and 3D color codes \cite{arxiv:2410.13568}.' - code_id: binary_linear detail: 'As CSS codes, variants of the 2D color code are constructed out of self-dual classical codes on cubic planar graphs \cite{doi:10.1016/0095-8956(91)90066-S}.' - code_id: hamiltonian diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml index 4d326f04e..4b5bb7af3 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml @@ -87,13 +87,13 @@ features: - 'Magic-state distillation protocols \cite{arxiv:1208.0928,arxiv:1209.0510,arxiv:2212.00813,arxiv:2403.03991} leading up to magic-state cultivation \cite{arxiv:2409.17595}.' - 'Framework of fault tolerance utilizing ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725} that is applicable to MBQC, FBQC, and conventional computation versions of the surface code \cite{arxiv:2303.08829}.' - 'Single-shot state preparation \cite{arxiv:1904.01502} and MWPM decoding \cite{arxiv:2209.09774}.' - - 'Syndrome extraction circuits consisting of CNOT gates and ancillary measurements \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield what is know as the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}.' + - 'Syndrome extraction circuits consisting of CNOT gates and ancillary measurements \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield what is know as the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.' decoders: - 'Using data from multiple syndrome measurements prior to decoding allows for correcting syndrome measurement errors. The surface code requires \hyperref[topic:asymptotics]{order} \(O(d)\) extraction rounds in order to gain a reliable estimate. Syndrome measurements are \hyperref[topic:effective-distance]{distance-preserving} because syndrome extraction circuits can be designed to avoid \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:quant-ph/0110143}.' - - 'Syndrome extraction circuits consist of CNOT gates and ancillary measurements since this is a stabilizer code \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}.' + - 'Syndrome extraction circuits consist of CNOT gates and ancillary measurements since this is a stabilizer code \cite{arxiv:1208.0928}. Measurement schedules can be optimized using spacetime circuit codes to yield the \textit{3CX surface code} \cite{arxiv:2302.02192}. Schedules can also be optimized via ZX calculus \cite{doi:10.1007/978-3-540-70583-3_25,arxiv:0906.4725}. Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed \cite{arxiv:2007.00307,arxiv:2206.12780,arxiv:2310.12981}, with the scheme in Ref. \cite{arxiv:2206.12780} being a special case of DWR.' - 'Expanding diamonds decoder correcting errors of some maximum fractal dimension \cite{manual:{Andrew Landahl, private communication, 2023}}. The sub-threshold failure probability scales as \((p/p_{\text{th}})^{d^\beta}\), where \(p_{\text{th}}\) is the threshold and \(\beta = \log_3 2\).' - 'Minimum weight perfect-matching (MWPM) \cite{arxiv:quant-ph/0110143,arxiv:1307.1740} (based on work by Edmonds on finding a matching in a graph \cite{doi:10.4153/CJM-1965-045-4,doi:10.6028/jres.069B.013}), which takes time up to polynomial in \(n\) for the surface code.