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valbert4 committed Nov 7, 2024
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6 changes: 3 additions & 3 deletions codes/quantum/properties/hamiltonian/commuting_projector.yml
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Expand Up @@ -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}.
Expand All @@ -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
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Expand Up @@ -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:
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2 changes: 1 addition & 1 deletion codes/quantum/properties/stabilizer/qldpc/qldpc.yml
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Expand Up @@ -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
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