Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory

DOI10.1016/S0003-4916(02)00019-2zbMath1023.81024arXivquant-ph/0207088OpenAlexW2107453273MaRDI QIDQ1867221

Jim Harrington, Chenyang Wang, John Preskill

Publication date: 2 April 2003

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0207088

zbMATH Keywords

Monte Carlo simulationsquenched disordermagnetic monopolesexcitationsNishimori linecritical concentration\(\pm J\) random-bond Ising model\(\pm J\) random-plaquette \(Z_2\) gauge modelelectric confinementHiggs phase transitionone-dimensional flux tubesstorage of quantum informationtopological error-correcting codes

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Quantum computation (81P68) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Yang-Mills and other gauge theories in quantum field theory (81T13) Strong interaction, including quantum chromodynamics (81V05) Phase transitions (general) in equilibrium statistical mechanics (82B26) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (20)

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice \(\pm J\) Ising model ⋮ Analyticity of the energy in an Ising spin glass with correlated disorder ⋮ Finite-size scaling in the energy-entropy plane for the 2D\(\pm J\) Ising spin glass ⋮ Finite-size scaling of the domain wall entropy distributions for the 2D\(\pm J\) Ising spin glass ⋮ Self-duality and phase structure of the 4D random-plaquette \(\mathbb Z_{2}\) gauge model ⋮ Correlation inequalities for the uniform eight-vertex model and the toric code model ⋮ Thermal states of anyonic systems ⋮ Cellular automaton decoders of topological quantum memories in the fault tolerant setting ⋮ New quantum surface codes from semi-regular tessellations ⋮ Homological error correction: Classical and quantum codes ⋮ Structure of 2D topological stabilizer codes ⋮ Toric codes and quantum doubles from two-body Hamiltonians ⋮ Long range failure-tolerant entanglement distribution ⋮ Subextensive singularity in the 2D \(\pm J\) Ising spin glass ⋮ Fast decoders for qudit topological codes ⋮ Aspect-ratio scaling of domain wall entropy for the 2D \(\pm J\) Ising spin glass ⋮ A fault-tolerant one-way quantum computer ⋮ Statistical mechanical models for quantum codes with correlated noise ⋮ Logical error rate scaling of the toric code ⋮ \(Z_{N}\) Gauge theories on a lattice and quantum memory

Cites Work

• Quantum computations: algorithms and error correction
• Error Correcting Codes in Quantum Theory
• Statistical Physics of Spin Glasses and Information Processing
• Topological quantum memory
• Paths, Trees, and Flowers
• Unnamed Item

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