Mixing Time of Open Quantum Systems via Hypocoercivity

Abstract

Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. This framework yields mixing time estimates for a class of quantum systems that are otherwise hard to analyze, even though it does not apply to arbitrary Lindbladians. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.

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Cited by in corpus (6)

• Rapid quantum ground state preparation via dissipative dynamics
• Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath