From 9959f1db53fe2ad82db5d3a9ff6b55bd4d8a2633 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Tue, 27 Aug 2024 17:44:09 -0400 Subject: [PATCH] color ref --- .../qubits/stabilizer/topological/color/3d_color/3d_color.yml | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml index b4c8cb4b9..c2b513d0a 100644 --- a/codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml +++ b/codes/quantum/qubits/stabilizer/topological/color/3d_color/3d_color.yml @@ -21,6 +21,8 @@ description: | features: transversal_gates: + - 'Transversal action of \(T\) gates on color codes on general 3-manifolds realizes a \(CCZ\) gate on three logical qubits and is related to a topological invariant that is called the triple intersection number \cite{arxiv:2310.16982}.' + - 'Transversal \(S\) gate on color codes on general 3-manifolds corresponds to a higher-form symmetry \cite{arxiv:2310.16982}.' - 'Universal transversal gates can be achieved using lattice surgery or code deformation \cite{arxiv:1006.5260,arxiv:0806.4827}.' general_gates: @@ -50,6 +52,8 @@ relations: This mapping can also be done via code concatenation \cite{arxiv:1801.04255}.' - code_id: xs_stabilizer detail: 'The 3D color code on a particular lattice 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: spt + detail: 'Transversal action of \(T\) gates on color codes on general 3-manifolds realizes a \(CCZ\) gate on three logical qubits and is related to a topological invariant that is called the triple intersection number \cite{arxiv:2310.16982}. Transversal \(S\) gate on color codes on general 3-manifolds corresponds to a higher-form symmetry \cite{arxiv:2310.16982}.' # Begin Entry Meta Information