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arXiv:2206.02456 · Physical Review Letters

Noise-Induced Quantum Synchronization

Finn Schmolke, Eric Lutz

Published Dec 16, 2022• 49 citations
arXivHTMLPDF

Abstract

Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.

DOI
10.1103/physrevlett.129.250601

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•Jan 1, 2012•0 citations
Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.
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. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system and uncover the potential role of synchronization for mixed-state quantum information science.
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 number-theoretic function involving the noise sites and the chain length. We derive a closed-form expression for local qubit observables restricted to the DFS and prove that stable synchronization of the edge qubits for arbitrary initial states occurs \textit{if and only if} the DFS supports exactly one single-excitation eigenstate. We further show that this same condition also guarantees constant asymptotic entanglement between the edge qubits, so that generic stable synchronization and constant asymptotic entanglement necessarily coexist. By contrast, when the DFS supports multiple single-excitation eigenstates, synchronization becomes initial state dependent and may be entirely absent, even though stable oscillatory entanglement can persist indefinitely.
Random fluctuations can lead to cooperative effects in complex systems. We here report the observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system, and initiate the exploration of collective synchronization effects with stronger than classical correlations.
We show that bipartite entanglement in an one-dimensional quantum spin model undergoing time evolution due to local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models including the anisotropic XYXYXY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZXXZXXZ model, the XYZXYZXYZ model, and the ${J}_{1}\ensuremath{-}{J}_{2}$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin chain, for example, in paramagnetic phases of the ATXY model, indicating a scale invariance. Freezing of entanglement is found to be robust against a change in the environment temperature, the presence of disorder in the system, and whether the noise is dissipative or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin pair from the noise source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.
We study defect generation in a quantum XY-spin chain arising due to the linear drive of the many-body Hamiltonian in the presence of a time-dependent fast Gaussian noise. The main objective of this work is to quantify analytically the effects of noise on the defect density production. In the absence of noise, it is well known that in the slow sweep regime, the defect density follows the Kibble-Zurek (KZ) scaling behavior with respect to the sweep speed. We consider time-dependent fast Gaussian noise in the anisotropy of the spin-coupling term $[{\ensuremath{\gamma}}_{0}=({J}_{1}\ensuremath{-}{J}_{2})/({J}_{1}+{J}_{2})]$ and show via analytical calculations that the defect density exhibits anti-Kibble-Zurek (AKZ) scaling behavior in the slow sweep regime. In the limit of large chain length and long time, we calculate the entropy and magnetization density of the final decohered state and show that their scaling behavior is consistent with the AKZ picture in the slow sweep regime. We have also numerically calculated the sublattice spin correlators for finite separation by evaluating the Toeplitz determinants and find results consistent with the KZ picture in the absence of noise, while in the presence of noise and slow sweep speeds the correlators exhibit the AKZ behavior. Furthermore, by considering the large nnn-separation asymptotes of the Toeplitz determinants, we further quantify the effect of the noise on the spin-spin correlators in the final decohered state. We show that while the correlation length of the sublattice correlator scales according to the AKZ behavior, we obtain different scaling for the magnetization correlators.
One of the central aims of quantum information theory is to exploit quantum mechanical phenomena such as superposition and entanglement to build a quantum computer — a device capable of effciently performing computational tasks which are not feasible on a classical computer. In order to achieve this goal it will be necessary to connect together the different components of a quantum computer with channels which are capable of quickly and faithfully transmitting quantum states. It has been suggested that a good channel for this purpose is a chain of permanently coupled quantum spins and we begin by reviewing some of the protocols which have been previously developed to transfer quantum information along such a spin chain. We then examine the effects of noise on the propagation of quantum information along spin chains, using a toolkit of methods which include Lieb-Robinson bounds, the Jordan-Wigner transform and correlation functions. Several fundamentally different noise models are considered including a static (time-independent) on-site disorder model and two different models of fluctuating (time-dependent) on-site disorder. Each noise model has a different and distinctive effect on the propagation of information — static disorder leads to exponential localisation whilst dynamic disorder can lead to diffusive or even ballistic propagation of information. We finish by reviewing how a spin chain (whether noisy or noise-free) can be viewed as a depolarising channel and we make a detailed study of the geometrical structure of all possible depolarising channels with respect to various bases, concentrating on the Pauli, Gell-Mann and Heisenberg-Weyl bases. In particular, we show precisely when the set of all possible depolarising channels forms a simplex in compression space.