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Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…
We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction…
Synchronization is ubiquitous in nature at various scales and fields. This phenomenon not only offers a window into the intrinsic harmony of complex systems, but also serves as a robust probe for many-body quantum systems. One such system…
The present study proposes a methodology that combines the 'Duffing oscillator system' and the 'Kuramoto oscillator network' to explore the synchronization of weak signals in dynamic systems. The first step of the procedure is to detect…
We study synchronization in the XX qubit chain subject to local or multi-local amplitude-damping noise. Analyzing the decoherence-free subspace (DFS) structure of the model, we show that it is completely determined by a simple…
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
In this work we investigate the stability of synchronized states for the Kuramoto model on scale-free and random networks in the presence of white noise forcing. We show that for a fixed coupling constant, the robustness of the globally…
The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that contrary to the impossibility of…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate…
The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We…
Josephson qubits without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an oscillator with adjustable frequency. The coupling between…
We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
Random fluctuations can lead to cooperative effects in complex systems. We here report the experimental observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions.…