From 8c88e9d12b72e3243b9ee704f0f9b32a47cb40a9 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 20 May 2024 22:08:06 -0400 Subject: [PATCH] topological stability refs --- codes/quantum/properties/block/topological/topological.yml | 4 ++++ .../quantum/properties/hamiltonian/commuting_projector.yml | 6 ++++++ .../lattice/translationally_invariant_stabilizer.yml | 3 --- .../qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml | 3 ++- 4 files changed, 12 insertions(+), 4 deletions(-) diff --git a/codes/quantum/properties/block/topological/topological.yml b/codes/quantum/properties/block/topological/topological.yml index 421a632b7..37e09ba2e 100644 --- a/codes/quantum/properties/block/topological/topological.yml +++ b/codes/quantum/properties/block/topological/topological.yml @@ -53,6 +53,10 @@ description: | # Frohlich braiding anyons doi:10.1142/S0129055X90000107, # Mention [39-41] in arxiv:2211.03798 +protection: | + Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds form a large class of topological phases. + They satisfy the topological order (TO) conditions \cite{arxiv:1001.4363,arxiv:1001.0344,arxiv:1109.1588,arxiv:1810.02428,arxiv:2010.15337}. + features: rate: 'The logical dimension \(K\) of 2D topological codes described by unitary modular fusion categories depends on the type of manifold \(\Sigma^2\) that is tesselated to form the many-body system. For closed orientable manifolds \cite{doi:10.1007/bf01217730,doi:10.1007/BF01238857}, diff --git a/codes/quantum/properties/hamiltonian/commuting_projector.yml b/codes/quantum/properties/hamiltonian/commuting_projector.yml index 0ab3753b7..80cc0a81d 100644 --- a/codes/quantum/properties/hamiltonian/commuting_projector.yml +++ b/codes/quantum/properties/hamiltonian/commuting_projector.yml @@ -11,12 +11,18 @@ name: 'Commuting-projector code' description: | Hamiltonian-based code whose Hamiltonian terms can be expressed as orthogonal projectors (i.e., Hermitian operators with eigenvalues 0 or 1) that commute with each other. +protection: | + Geometrically local commuting-projector code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the TO 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}. + relations: parents: - code_id: hamiltonian + 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 TO 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}.' # 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 003e3d04b..022162de6 100644 --- a/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml +++ b/codes/quantum/properties/stabilizer/lattice/translationally_invariant_stabilizer.yml @@ -66,9 +66,6 @@ relations: detail: 'Lattice stabilizer codes are QLDPC codes on Euclidean geometries.' - code_id: quantum_quasi_cyclic detail: 'Lattice stabilizer codes are invariant under translations by a lattice unit cell.' - cousins: - - code_id: hamiltonian - detail: 'Lattice stabilizer code Hamiltonians are stable with respect to small perturbations \cite{arxiv:1001.4363,arxiv:1001.0344}, meaning that the notion of a phase can be defined.' diff --git a/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml b/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml index e7115f801..ed0554f8b 100644 --- a/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml +++ b/codes/quantum/qubits/subsystem/qldpc/bacon_shor/bacon_shor.yml @@ -96,7 +96,8 @@ relations: detail: 'A compass code on a fully non-colored lattice reduces to the Bacon-Shor code.' 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}.' + detail: 'The 2D Bacon-Shor gauge-group Hamiltonian is the compass model \cite{doi:10.1070/PU1982v025n04ABEH004537,arxiv:cond-mat/0501708,arxiv:1303.5922}. + Bacon-Show code Hamiltonians can be used to suppress errors in adiabatic quantum computation \cite{arxiv:1511.01997}, while subspace-code two-local Hamiltonians cannot \cite{arxiv:1410.5487}.' - code_id: floquet detail: 'The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule \cite{arxiv:2403.03291}.'