Quantum synchronization: A tutorial guide

• URL: http://arxiv.org/abs/2609.14375v1
• Date: Sun, 13 Sep 2026 08:11:19 GMT
• Title: Quantum synchronization: A tutorial guide
• Abstract summary: This tutorial review offers a systematic framework for analyzing synchronization in classical and quantum dynamical systems.<n>Starting from amplitude-phase dynamics, we introduce topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model.<n>We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.

Related papers

• Second harmonic phase locking and synchronization blockade in quadratically coupled driven quantum van der Pol oscillators [0.0]
  We investigate the dynamics of a quadratically coupled system under the influence of an external drive applied to the second oscillator.<n>Our analysis reveals a synchronization blockade, characterized by the complete suppression of conventional 1:1 phase-locking with the drive.<n>A classical mean-field analysis of the corresponding equations of motion reproduces this asymmetric phase-locking geometry.
  arXiv  Detail & Related papers  (2026-08-29T10:36:42Z)
• Learnable yet not simulable: a quantum resource theory of learning models [57.695822250391906]
  It remains unclear which quantum resource governs the classical learnability of quantum circuits.<n>We study the expectation-value functions of families of tunable quantum circuits.<n>These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning.
  arXiv  Detail & Related papers  (2026-08-03T14:48:03Z)
• Synchronization in the quantum regime [0.0]
  Can synchronization, the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems, also occur in the quantum regime?<n> Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level.<n>We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations to genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
  arXiv  Detail & Related papers  (2026-06-19T08:46:04Z)
• Quantum Clock Synchronization Networks: A Survey [44.015977790437454]
  Quantum clock synchronization (QCS) aims to establish a shared temporal reference between distant nodes.<n>QCS protocols offer the potential to surpass classical precision bounds and enhance resilience against adversarial manipulations.<n>This survey provides a unified and critical overview of the rapidly growing QCS research landscape.
  arXiv  Detail & Related papers  (2026-04-06T05:30:54Z)
• Observation of synchronization between two quantum van der Pol oscillators in trapped ions [3.7967008906519513]
  Synchronization is a hallmark of nonlinear dynamics and drives self-organized behavior across systems.<n>Here, we demonstrate synchronization between two quantum van der Pol oscillators using trapped ions.<n>Our results establish limit-cycle synchronization in the quantum regime and pave the way toward exploring complex synchronized dynamics in larger networks.
  arXiv  Detail & Related papers  (2025-09-22T21:05:46Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.<n>We find sufficient conditions under which dynamical decoupling works for such systems.<n>Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Role of Coherence and Degeneracies in Quantum Synchronisation [0.0]
  We study quantum synchronisation by utilising Liouville space perturbation theory. We first clarify the role of centers, symmetries and oscillating coherences in the context of quantum synchronisation. We then analyse the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system.
  arXiv  Detail & Related papers  (2021-04-09T14:13:39Z)
• 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)
• Synchronisation phase as an indicator of persistent quantum correlations between subsystems [68.8204255655161]
  Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. We show that our analysis applies to a variety of spontaneously synchronising open quantum systems.
  arXiv  Detail & Related papers  (2020-06-29T17:21:32Z)

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.