From 83c2c696b5a62775b6c8e8a1e936ec049b52cdec Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Fri, 3 Jan 2025 17:05:27 -0500 Subject: [PATCH] refs --- codes/quantum/properties/hamiltonian/self_correct.yml | 1 + codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml | 2 +- .../stabilizer/topological/surface/2d_surface/surface.yml | 2 +- 3 files changed, 3 insertions(+), 2 deletions(-) diff --git a/codes/quantum/properties/hamiltonian/self_correct.yml b/codes/quantum/properties/hamiltonian/self_correct.yml index 1cbe1e2a5..8514008e4 100644 --- a/codes/quantum/properties/hamiltonian/self_correct.yml +++ b/codes/quantum/properties/hamiltonian/self_correct.yml @@ -44,6 +44,7 @@ protection: | 2D stabilizer codes \cite{arxiv:0810.1983} and encodings of frustration-free code Hamiltonians \cite{arxiv:1209.5750} admit only constant-energy excitations, and so do not have an energy barrier. There exist several candidates for self-correction as well as several partially self-correcting memories (see cousins below). + The lifetime of a ground-state memory protected by a Hamiltonian alone can increase at most logarithmically with \(n\) under depolarizing noise \cite{arxiv:0807.0287,arxiv:0904.4861}, and a clock Hamiltonian can saturate this bound \cite{arxiv:0904.4861}. notes: - 'Reviews of self-correcting memories \cite{arxiv:1210.3207,arxiv:1411.6643}.' diff --git a/codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml b/codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml index af8181948..be523c6fc 100644 --- a/codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml +++ b/codes/quantum/properties/stabilizer/lattice/2d_stabilizer.yml @@ -20,7 +20,7 @@ features: decoders: - 'Renormalization group (RG) decoder \cite{arxiv:1006.1362}.' - 'Tensor-network based decoder for 2D codes subject to correlated noise \cite{arxiv:1809.10704}.' - - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2211.09803,arxiv:2401.06300,arxiv:2402.14906}; see also Refs. \cite{arxiv:0911.3843,arxiv:1107.3940}.' + - 'Standard stabilizer-based error correction can be performed even in the presence of perturbations to the codespace \cite{arxiv:2211.09803,arxiv:2401.06300,arxiv:2402.14906}; see also Refs. \cite{arxiv:0807.0287,arxiv:0911.3843,arxiv:1107.3940}.' code_capacity_threshold: - 'Noise thresholds can be formulated as anyon \hyperref[topic:code-switching]{condensation} transitions in a topological field theory \cite{arxiv:2301.05687}, generalizing the mapping of the effect of noise on a code state to a statistical mechanical model \cite{arxiv:quant-ph/0110143,arxiv:1208.2317,arxiv:1311.7688,arxiv:1809.10704}. Namely, the noise threshold for a noise channel \(\cal{E}\) acting on a 2D stabilizer state \(|\psi\rangle\) can be obtained from the properties of the resulting (mixed) state \(\mathcal{E}(|\psi\rangle\langle\psi|)\) \cite{arxiv:2301.05238,arxiv:2301.05687,arxiv:2301.05689,arxiv:2309.11879, arxiv:2401.17359}.' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml index d62fc26fd..fac75fd84 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml @@ -37,7 +37,7 @@ protection: | The joint \(+1\)-eigenspace of the \(Z\)-type Paulis corresponds to the subspace that conserves \(\mathbb{Z}_2\) flux, while the joint \(+1\)-eigenspace of \(X\)-type operators corresponds to the subspace that preserves \(\mathbb{Z}_2\) gauge symmetry (a one-form symmetry). Logical Pauli operators correspond to non-contractible Wilson loops in the case of closed boundaries, and to paths connecting different types of boundaries in the case of open boundaries. - Behavior under Hamiltonian \(X\)-type and \(Z\)-type perturbations is related to an anisotropic 3D gauge Higgs model \cite{arxiv:0804.3175,arxiv:1411.5815}. + Behavior under Hamiltonian \(X\)-type and \(Z\)-type perturbations is related to an anisotropic 3D gauge Higgs model \cite{arxiv:cond-mat/0609048,arxiv:0804.3175,arxiv:0807.0487,arxiv:1411.5815}. In order to corrupt logical states, any local noise must bring the code state out of the topological order \cite{arxiv:2310.08639}. Alternatively, there is a general correspondence between stabilizer codes and gauge theory, with the stabilizer group playing the role of the gauge group \cite{arxiv:2412.15317}.