diff --git a/codes/quantum/properties/hamiltonian/commuting_projector.yml b/codes/quantum/properties/hamiltonian/commuting_projector.yml index 562572900..93ed52588 100644 --- a/codes/quantum/properties/hamiltonian/commuting_projector.yml +++ b/codes/quantum/properties/hamiltonian/commuting_projector.yml @@ -13,7 +13,7 @@ description: | protection: | Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}. - This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC exhibiting check soundness \cite{arxiv:2411.01002}. + This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}). 2D topological order on qubit manifolds requires weight-four Hamiltonian terms, i.e., it cannot be stabilized via weight-two or weight-three terms on nearly Euclidean geometries of qubits or qutrits \cite{arxiv:quant-ph/0308021,arxiv:1102.0770,arxiv:1803.02213}. Hamiltonians with weight-two (two-body) terms cannot be used for suppressing errors \cite{arxiv:1410.5487}. @@ -23,11 +23,11 @@ relations: parents: - code_id: hamiltonian detail: 'Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}. - This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC exhibiting check soundness \cite{arxiv:2411.01002}.' + This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).' cousins: - code_id: topological detail: 'Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}. - This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC exhibiting check soundness \cite{arxiv:2411.01002}.' + This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).' # Begin Entry Meta Information diff --git a/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml b/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml index 52017065d..2a6adc701 100644 --- a/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml +++ b/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml @@ -63,6 +63,7 @@ features: decoders: - 'Clustering decoder \cite{doi:10.7907/AHMQ-EG82,arxiv:1112.3252}.' - 'Quantum neural-network (QNN) decoder \cite{arxiv:2401.06300}.' + - 'Almost linear-time decoder \cite{arxiv:2411.02928}.' relations: parents: diff --git a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml b/codes/quantum/properties/stabilizer/qldpc/qldpc.yml index d086c1170..ac0a0fb77 100644 --- a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml +++ b/codes/quantum/properties/stabilizer/qldpc/qldpc.yml @@ -133,7 +133,7 @@ relations: - code_id: ldpc - code_id: topological detail: 'Topological codes are not generally defined using Pauli strings. However, for appropriate tesselations, the codespace is the ground-state subspace of a geometrically local Hamiltonian. In this sense, topological codes are QLDPC codes. Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the \hyperref[topic:tqo]{TQO conditions}, meaning that a notion of a phase can be defined \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}. - This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC exhibiting check soundness \cite{arxiv:2411.01002}.' + This notion can be extended to semi-hyperbolic manifolds \cite{arxiv:2405.19412} and non-geometrically local QLDPC codes exhibiting check soundness \cite{arxiv:2411.01002} (see also \cite{arxiv:2411.02384}).' - code_id: dynamic_gen detail: 'QLDPC codes can arise from a dynamical process \cite{arxiv:2004.09560}.' - code_id: hamiltonian