From 9e05641ed5bd8494a548b39aa2ec172ff641cb34 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Sun, 10 Mar 2024 19:36:23 -0600 Subject: [PATCH] stellated color --- .../small_distance/small/stab_4_2_2.yml | 7 ++-- .../topological/color/2dcolor/2d_color.yml | 3 +- .../stabilizer/topological/color/3d_color.yml | 5 +++ .../topological/color/stellated_color.yml | 33 +++++++++++++++++++ .../surface/non-css/twist_defect_surface.yml | 4 ++- .../surface/two_dim/surface/surface.yml | 2 +- .../topological/compass/bacon_shor.yml | 2 ++ 7 files changed, 49 insertions(+), 7 deletions(-) create mode 100644 codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml diff --git a/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml b/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml index 85ce7b9d1..ee6f6397b 100644 --- a/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml +++ b/codes/quantum/qubits/small_distance/small/stab_4_2_2.yml @@ -69,7 +69,8 @@ relations: - code_id: surface detail: '\([[4,2,2]]\) code is the smallest toric code.' - code_id: triangular_color - detail: '\([[4,2,2]]\) code can be interpreted as a small rectangular color code on a trapezoidal patch of four qubits that makes up two-thirds of a hexagon \cite{arxiv:2212.00042,arxiv:2305.13581}.' + detail: '\([[4,2,2]]\) code can be interpreted as a small rectangular color code on a trapezoidal patch of four qubits that makes up two-thirds of a hexagon \cite{arxiv:2212.00042,arxiv:2305.13581}. + A small triangular color code is a \([[4,1,2]]\) code with three weight-three stabilizer generators \cite[Fig. 7]{arxiv:1806.02820}.' - code_id: ball_color detail: 'The \([[4,2,2]]\) code is a hyperoctahedron code for \(D=2\).' - code_id: iceberg @@ -91,9 +92,7 @@ relations: - code_id: binomial detail: '\([[4,1,2]]\) subcode consisting of \(\{|\overline{00}\rangle\) and any other codeword reduces to the \(0,2,4\) binomial code when the basis labels in each codeword are written as in base-ten. Such a mapping can be generalized \cite{manual:{Linshu Li, private communication, 2018}}.' - code_id: heavy_hex - detail: 'Magic states prepared using the \([[4,1,2]]\) subcode can be injected into a largest heavy-hex code \cite{arxiv:2110.04285,arxiv:2305.13581}.' - - code_id: quantum_concatenated - detail: 'Concatenating \([[4,2,2]]\) code with surface code can generate 2D topological code with a reasonable circuit-based threshold \cite{doi:10.26421/QIC16.15-16-1}.' + detail: 'Magic states prepared using the \([[4,1,2]]\) subcode can be injected into the heavy-hex code \cite{arxiv:2110.04285,arxiv:2305.13581}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/stabilizer/topological/color/2dcolor/2d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2dcolor/2d_color.yml index 2eafc5158..2b020569a 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/2dcolor/2d_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/2dcolor/2d_color.yml @@ -65,7 +65,8 @@ relations: cousins: - code_id: surface detail: 'The 2D color code is equivalent to multiple decoupled copies of the 2D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}. - 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 hexagonal directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}.' + 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 hexagonal directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}. + Concatenating the \([[4,2,2]]\) code with the surface code is equivalent to removing stabilizer generators from the 4.8.8 color code \cite{doi:10.26421/QIC16.15-16-1}.' - code_id: 3d_color detail: 'Gauge fixing can be used to switch between 2D and 3D color codes, thereby yielding fault-tolerant with constant time overhead using only local quantum operations \cite{arxiv:1412.5079}.' diff --git a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml index b59e2a3a5..6625f08eb 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml @@ -13,6 +13,7 @@ introduced: '\cite{arxiv:cond-mat/0607736}' description: | Three-dimensional version of the color code. + Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and/or any twist defects \cite{arxiv:1806.02820} present. features: transversal_gates: 'Universal transversal gates can be achieved using lattice surgery \cite{arXiv:1407.5103} or code deformation \cite{arxiv:1006.5260,arXiv:0806.4827}.' @@ -33,6 +34,10 @@ relations: cousins: - code_id: 3d_surface detail: 'The 3D color code is equivalent to multiple decoupled copies of the 3D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.' + - code_id: xs_stabilizer + detail: 'The 3D color code admits XS stabilizers; see \href{https://www.youtube.com/watch?v=B8h5-ANc_-8}{talk by M. Kesselring at the 2020 FTQC conference}.' + - code_id: three_fermion + detail: 'The 3D color code is equivalent to two decoupled copies of the 3F code \cite[Appx. B]{arxiv:1806.02820}.' # Begin Entry Meta Information diff --git a/codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml b/codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml new file mode 100644 index 000000000..7f3cd0178 --- /dev/null +++ b/codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml @@ -0,0 +1,33 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: stellated_color +physical: qubits +logical: qubits + +name: 'Stellated color code' +introduced: '\cite{arxiv:1806.02820}' + +description: | + A color code on a lattice patch with a single twist defect at the center of the patch. + +features: + rate: 'Stellated color codes have negative curvature around the central defect, and thus circumvent the \hyperref[topic:BPT-bound]{BPT bound} for codes on Euclidean lattices.' + +relations: + parents: + - code_id: color + cousins: + - code_id: twist_defect_surface + detail: 'Stellated color codes are color-code analogues of twist-defect surface codes in that both encode logical information in lattice defects. + Instances of the former can be obtained by fattening \cite{arxiv:cond-mat/0607736} the vertices of the latter \cite{arxiv:1806.02820}.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2024-03-10' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/non-css/twist_defect_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/non-css/twist_defect_surface.yml index 2223df935..d59fca09a 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/non-css/twist_defect_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/non-css/twist_defect_surface.yml @@ -9,7 +9,7 @@ logical: qubits name: 'Twist-defect surface code' introduced: | - \cite{arxiv:1004.1838,arxiv:1612.04795,arxiv:2101.09349} + \cite{arxiv:1004.1838,arxiv:1612.04795,arxiv:1806.02820,arxiv:2101.09349} description: | A non-CSS extension of the 2D surface-code construction whose non-CSS stabilizer generators are associated with twist defects of the associated lattice. @@ -24,6 +24,8 @@ protection: | Code properties depends on the number and size of the twist defects. features: + rate: 'Twist-defect surface codes have negative curvature around their defects, and thus circumvent the \hyperref[topic:BPT-bound]{BPT bound} for codes on Euclidean lattices.' + general_gates: - | Clifford gates can be implemented via twist-based lattice surgery \cite{arxiv:2201.05678} or braiding defects diff --git a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml index ad722cd3f..4b0b16477 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/two_dim/surface/surface.yml @@ -142,7 +142,7 @@ features: - '\(0.5-2.9\%\) for various noise circuit-level noise models \cite{arxiv:0803.0272,arxiv:0811.0464} (see also Refs. \cite{arXiv:quant-ph/0207088,arXiv:1311.5003}).' - 'Quasistatic phase damping and readout noise: \(2.85\%\) \cite{arxiv:2401.04530}.' - 'The toric code has a \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.' - + - 'Circuit-based threshold of \(0.41\%\) when concatenated with the \([[4,2,2]]\) code \cite{doi:10.26421/QIC16.15-16-1}.' realizations: diff --git a/codes/quantum/qubits/subsystem/topological/compass/bacon_shor.yml b/codes/quantum/qubits/subsystem/topological/compass/bacon_shor.yml index 479119fb4..139e7180c 100644 --- a/codes/quantum/qubits/subsystem/topological/compass/bacon_shor.yml +++ b/codes/quantum/qubits/subsystem/topological/compass/bacon_shor.yml @@ -91,6 +91,8 @@ relations: cousins: - code_id: hamiltonian detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}.' + - code_id: floquet + detail: 'The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule \cite{arxiv:2403.03291}.' # Begin Entry Meta Information