Quantum Gibbs samplers: the commuting case

DOI10.1007/s00220-016-2641-8zbMath1386.82011arXiv1409.3435OpenAlexW2964257079WikidataQ59711911 ScholiaQ59711911MaRDI QIDQ2630727

Michael J. Kastoryano, Fernando G. S. L. Brandão

Publication date: 21 July 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3435

Mathematics Subject Classification ID

Quantum computation (81P68) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Cites Work

• Stability of frustration-free Hamiltonians
• Thermalization and canonical typicality in translation-invariant quantum lattice systems
• Thermalization time bounds for Pauli stabilizer Hamiltonians
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Generators of dynamical semigroups
• Finitely correlated states on quantum spin chains
• Hypercontractivity in noncommutative \(L_1\) spaces
• Relaxed criteria of the Dobrushin-Shlosman mixing condition
• For 2-D lattice spin systems weak mixing implies strong mixing
• The spectral gap for a Glauber-type dynamics in a continuous gas
• The spectral gap for some spin chains with discrete symmetry breaking
• Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets.
• Stability of local quantum dissipative systems
• Quantum information theory and quantum statistics.
• Gibbs states of a one dimensional quantum lattice
• Hypercontractivity of quasi-free quantum semigroups
• Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
• Quantum Hamiltonian Complexity
• On thermalization in Kitaev's 2D model
• The Markov chain Monte Carlo revolution
• Monte Carlo Simulation in Statistical Physics
• Dissipative dynamics for quantum spin systems on a lattice
• Séminaire de Probabilités XXXVI
• QUANTUM STOCHASTIC DYNAMICS II
• Topological quantum memory
• Quantum equilibration in finite time
• The detectability lemma and quantum gap amplification
• The $\chi ^2$χ2-divergence and mixing times of quantum Markov processes
• On Thermal Stability of Topological Qubit in Kitaev's 4D Model
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Rapid mixing implies exponential decay of correlations
• Lower bounds to the spectral gap of Davies generators
• Quantum rejection sampling
• The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
• Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields
• Observables at infinity and states with short range correlations in statistical mechanics
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