Mixing Time of Open Quantum Systems via Hypocoercivity

• URL: http://arxiv.org/abs/2404.11503v1
• Date: Wed, 17 Apr 2024 15:58:17 GMT
• Title: Mixing Time of Open Quantum Systems via Hypocoercivity
• Authors: Di Fang, Jianfeng Lu, Yu Tong,
• Abstract summary: Existing approaches for estimating the mixing time of open quantum systems often rely on the spectral gap estimation of the Lindbladian generator. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.
• Score: 5.327284412522592
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.

Related papers

• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential [0.0]
  The Schr"odinger equation is a fundamental equation in quantum mechanics. Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
  arXiv  Detail & Related papers  (2024-08-04T13:11:52Z)
• Liouvillian-gap analysis of open quantum many-body systems in the weak dissipation limit [2.7195102129095003]
  We conjecture that a singularity is generic in bulk-dissipated quantum many-body systems. This conjecture suggests that the many-body Lindblad equation in the weak dissipation regime contains nontrivial information on intrinsic properties of a quantum many-body system.
  arXiv  Detail & Related papers  (2023-11-17T03:31:09Z)
• Testing Quantum Gravity using Pulsed Optomechanical Systems [13.650870855008112]
  We consider the Schr"odinger-Newton (SN) theory and the Correlated Worldline (CWL) theory, and show that they can be distinguished from conventional quantum mechanics. We find that discriminating between the theories will be very difficult until experimental control over low frequency quantum optomechanical systems is pushed further.
  arXiv  Detail & Related papers  (2023-11-03T17:06:57Z)
• Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System [0.3495246564946556]
  We present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems.
  arXiv  Detail & Related papers  (2023-09-06T03:53:09Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Quantum estimation of a time dependent perturbation [0.0]
  We analyze the estimation of a time dependent perturbation acting on a quantum system. We combine quantum measurement theory and classical filter theory into a time evolving hybrid quantum and classical trajectory.
  arXiv  Detail & Related papers  (2021-06-06T12:11:39Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.