A statistical mechanics view on Kitaev's proposal for quantum memories

Abstract

We compute rigorously the ground and equilibrium states for Kitaev's model in 2D, both the finite and infinite version, using an analogy with the 1D Ising ferromagnet. Next, we investigate the structure of the reduced dynamics in the presence of thermal baths in the Markovian regime. Special attention is paid to the dynamics of the topological freedoms which have been proposed for storing quantum information.

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Cited by in corpus (57)

• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Quantum memories at finite temperature
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• Entanglement and topological entropy of the toric code at finite temperature
• On thermalization in Kitaev's 2D model
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Completely positive master equation for arbitrary driving and small level spacing
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Simulations of quantum double models
• Toric-boson model: Toward a topological quantum memory at finite temperature
• Kitaev's quantum double model as an error correcting code
• Local topological order inhibits thermal stability in 2D
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Topological order and topological entropy in classical systems
• Topological Order Following a Quantum Quench
• Localization of Toric Code Defects
• Localized endomorphisms in Kitaev's toric code on the plane
• Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid
• Enhanced thermal stability of the toric code through coupling to a bosonic bath
• Quantum spin systems on infinite lattices
• Quantum memories and error correction
• Haag duality for Kitaev's quantum double model for abelian groups
• Universality Classes of Stabilizer Code Hamiltonians
• Haag duality and the distal split property for cones in the toric code
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Fracton Topological Order at Finite Temperature
• Renormalization group decoder for a four-dimensional toric code
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• On the stability of charges in infinite quantum spin systems
• Dynamic Generation of Topologically Protected Self-Correcting Quantum Memory
• Topological order, entanglement, and quantum memory at finite temperature
• Kitaev's quantum double model from a local quantum physics point of view
• Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime
• Active error correction for Abelian and non-Abelian anyons
• Kosaki-Longo index and classification of charges in 2D quantum spin models
• Finite temperature quantum simulation of stabilizer Hamiltonians
• Remarks on anomalous symmetries of C*-algebras
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Decoherence and Entanglement Dynamics of Coupled Qubits
• Novel Topological Phases and Self-Correcting Memories in Interacting Anyon Systems
• Low-temperature coherence properties of Z_2 quantum memory
• Decay of fidelity in terms of correlation functions
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• A dynamical Toric Code model with fusion and de-fusion
• Dynamical abelian anyons with bound states and scattering states
• An algebraic quantum field theoretic approach to toric code with gapped boundary
• Local topological order and boundary algebras
• Homological codes and abelian anyons
• Thermal stability of two-dimensional Topological Color Code
• Topologically ordered states in infinite quantum spin systems
• Quantum memories and Landauer's principle
• Classification of the anyon sectors of Kitaev's quantum double model
• On a C*-Diagonal Generated by the Toric Code
• Global estimates of errors in quantum computation by the Feynman-Vernon formalism
• Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions