Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks

• URL: http://arxiv.org/abs/2402.00792v1
• Date: Thu, 1 Feb 2024 17:23:32 GMT
• Title: Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks
• Authors: Eliana Fiorelli
• Abstract summary: We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We apply our results to quantum generalized Hopfield associative memories, showing that, asymptotically and at the mesoscopic scale only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.

Related papers

• Quantum ergodicity and scrambling in quantum annealers [0.0]
  We show that the unitary evolution operator describing the complete dynamics of quantum annealers is typically highly quantum chaotic. We observe that the Heisenberg dynamics of a quantum annealer leads to extensive operator spreading, a hallmark of quantum information scrambling.
  arXiv  Detail & Related papers  (2024-11-19T16:34:35Z)
• Precision bounds for multiple currents in open quantum systems [37.69303106863453]
  We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics. Our bounds are tighter than previously derived quantum TURs and KURs for single observables. We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
  arXiv  Detail & Related papers  (2024-11-13T23:38:24Z)
• Quantum coarsening and collective dynamics on a programmable quantum simulator [27.84599956781646]
  We experimentally study collective dynamics across a (2+1)D Ising quantum phase transition. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode.
  arXiv  Detail & Related papers  (2024-07-03T16:29:12Z)
• Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
  We develop a general approach to the dynamics of quantum/classical systems. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
  arXiv  Detail & Related papers  (2024-03-24T08:26:54Z)
• 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)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application [0.0]
  We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models.
  arXiv  Detail & Related papers  (2023-02-08T15:58:39Z)
• Learning in quantum games [41.67943127631515]
  We show that the induced quantum state dynamics decompose into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues. We find that the FTQL dynamics incur no more than constant regret in all quantum games.
  arXiv  Detail & Related papers  (2023-02-05T08:23:04Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)

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.