From 2fbb00cb9d76c769dd732e0879c352200a2c44c0 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Tue, 27 Aug 2024 18:40:47 -0400 Subject: [PATCH] quasi_hyperbolic_color --- .../magic/k-orthogonal/quantum_rainbow.yml | 2 +- .../topological/color/hyperbolic_color.yml | 12 +++--- .../color/quasi_hyperbolic_color.yml | 42 +++++++++++++++++++ .../surface/hyperbolic/hyperbolic_surface.yml | 3 +- 4 files changed, 49 insertions(+), 10 deletions(-) create mode 100644 codes/quantum/qubits/stabilizer/topological/color/quasi_hyperbolic_color.yml diff --git a/codes/quantum/qubits/stabilizer/magic/k-orthogonal/quantum_rainbow.yml b/codes/quantum/qubits/stabilizer/magic/k-orthogonal/quantum_rainbow.yml index c3c994c14..3603a5fb3 100644 --- a/codes/quantum/qubits/stabilizer/magic/k-orthogonal/quantum_rainbow.yml +++ b/codes/quantum/qubits/stabilizer/magic/k-orthogonal/quantum_rainbow.yml @@ -28,7 +28,7 @@ relations: detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.' - code_id: quantum_triorthogonal detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes \cite{arxiv:2310.16982} yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.' - - code_id: hyperbolic_color + - code_id: quasi_hyperbolic_color detail: 'Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the \term{Clifford hierarchy}. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) \cite{arxiv:2408.13130}.' diff --git a/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml b/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml index 7b710d86b..b6651e86b 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/hyperbolic_color.yml @@ -15,7 +15,6 @@ description: | As opposed to there being only three types of uniform three-valent and three-colorable lattice tilings in the 2D Euclidean plane, there is an infinite number of admissible hyperbolic tilings in the 2D hyperbolic plane \cite{arxiv:1804.06382}. Certain double covers of hyperbolic tilings also yield admissible tilings \cite{arxiv:1301.6588}. Other admissible hyperbolic tilings can be obtained via a fattening procedure \cite{arxiv:cond-mat/0607736}; see also a construction based on the more general quantum pin codes \cite{arxiv:1906.11394}. - See Ref. \cite{arxiv:2310.16982} for surface codes on quasi-hyperbolic manifolds. protection: | The use of hyperbolic surfaces allows one to circumvent bounds on code parameters (such as the \term{BPT bound}) that are valid for lattice geometries. @@ -23,14 +22,9 @@ protection: | For example, a \(\{4g,4g\}\) tiling with periodic boundary conditions (i.e., a \(g\)-torus) yields a \([[4g+8,4g,4]]\) code family \cite{arxiv:1804.06382}. More examples, such as the \([[160,20,8]]\) code on the 4.10.10 tiling, are provided in \cite[Sec. V.A]{arxiv:1906.11394}. - There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}. - A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}. - 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 \(1 - 1/\ell - 1/m\). A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.' + rate: 'In the double-cover construction \cite{arxiv:1301.6588}, an \(\{\ell,m\}\) input tiling yields a code family with an asymptotic rate of \(1 - 1/\ell - 1/m\).' - fault_tolerance: - - 'There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}. A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.' relations: @@ -46,5 +40,9 @@ relations: _meta: # Change log - most recent first changelog: + - user_id: GuanyuZhu + date: '2024-08-27' + - user_id: VictorVAlbert + date: '2024-08-27' - user_id: VictorVAlbert date: '2024-04-02' diff --git a/codes/quantum/qubits/stabilizer/topological/color/quasi_hyperbolic_color.yml b/codes/quantum/qubits/stabilizer/topological/color/quasi_hyperbolic_color.yml new file mode 100644 index 000000000..94fcd4f45 --- /dev/null +++ b/codes/quantum/qubits/stabilizer/topological/color/quasi_hyperbolic_color.yml @@ -0,0 +1,42 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: quasi_hyperbolic_color +physical: qubits +logical: qubits + +name: 'Quasi-hyperbolic color code' +introduced: '\cite{arxiv:2310.16982}' + +description: | + An extension of the color code construction to quasi-hyperbolic manifolds, e.g., a product of a 2D hyperbolic surface and a circle. + +protection: | + There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}. + A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}. + +features: + rate: 'A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.' + + fault_tolerance: + - 'There exists a family with rate of \hyperref[topic:asymptotics]{order} \(O(1/\log n)\) and minimum distance of \hyperref[topic:asymptotics]{order} \(\Omega(\log n)\) which supports fault-tolerant non-Clifford gates \cite{arxiv:2310.16982}. A construction based on the Torelli mapping yields a code with constant rate with similar gates \cite{arxiv:2310.16982}.' + + +relations: + parents: + - code_id: color + cousins: + - code_id: higher_dimensional_surface + detail: 'Quasi-hyperbolic color codes are related to quasi-hyperbolic surface codes via a constant-depth Clifford circuit \cite{arxiv:2310.16982}.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: GuanyuZhu + date: '2024-08-27' + - user_id: VictorVAlbert + date: '2024-08-27' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/hyperbolic/hyperbolic_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/hyperbolic/hyperbolic_surface.yml index df78ccb4d..b42562d72 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/hyperbolic/hyperbolic_surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/hyperbolic/hyperbolic_surface.yml @@ -12,8 +12,7 @@ name: 'Hyperbolic surface code' description: | An extension of the Kitaev surface code construction to hyperbolic manifolds. Given a cellulation of a manifold, qubits are put on \(i\)-dimensional faces, \(X\)-type stabilizers are associated with \((i-1)\)-faces, while \(Z\)-type stabilizers are associated with \(i+1\)-faces. - See Ref. \cite{arxiv:2310.16982} for surface codes on quasi-hyperbolic manifolds. - + protection: 'Constructions (see code children below) have yielded distances scaling favorably with the number of qubits. The use of hyperbolic surfaces allows one to circumvent bounds on code parameters (such as the \term{BPT bound}) that are valid for lattice geometries.' features: