2,317 research outputs found

    Characterizing dynamics with covariant Lyapunov vectors

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    A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.Comment: 4 pages, 3 figures, submitted to Physical Review letter

    Phase space geometry and optimal state preparation in quantum metrology with collective spins

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    We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative predictions of the timescales required to prepare various metrologically useful states, and that these predictions remain accurate even for moderate system sizes, surprisingly far from the classical limit. Furthermore, this framework allows us to build a geometric picture that relates optimal (exponentially fast) entangled probe preparation to the existence of separatrices connecting saddle points in phase space. We illustrate our results with the paradigmatic examples of the two-axis counter-twisting and twisting-and-turning Hamiltonians, where we provide analytical expressions for all the relevant optimal time scales. Finally, we propose a generalization of these models to include pp-body collective interaction (or pp-order twisting), beyond the usual case of p=2p=2. Using our geometric framework, we prove a no-go theorem for the local optimality of these models for p>2p>2.Comment: 15 pages, 6 figures, 9 pages appendi

    Simulation of complex dynamics of mean-field pp-spin models using measurement-based quantum feedback control

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    We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Mu\~noz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as pp-spin Hamiltonians, which describe Ising-like models on a completely connected graph with pp-body interactions. The method simulates the desired mean field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the pp-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter pp. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.Comment: 16 pages, 7 figure

    Simulating nonlinear dynamics of collective spins via quantum measurement and feedback

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    We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.Comment: 6 pages, 4 figures and supplementary materia

    Circuit Complexity Meets Ontology-Based Data Access

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    Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without any use of theory. Thus the problem reduces to the standard database setting. However, the size of the query may increase substantially during the reformulation. In this survey we review a recently developed framework on proving lower and upper bounds on the size of this reformulation by employing methods and results from Boolean circuit complexity.Comment: To appear in proceedings of CSR 2015, LNCS 9139, Springe

    On the succinctness of query rewriting over shallow ontologies

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    We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existential rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of conjunctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP ïżœis included in P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable

    Fast cerebellar reflex circuitry requires synaptic vesicle priming by Munc13-3

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    Munc13-3 is a member of the Munc13 family of synaptic vesicle priming proteins and mainly expressed in cerebellar neurons. Munc13-3 null mutant (Munc13-3(−/−)) mice show decreased synaptic release probability at parallel fiber to Purkinje cell, granule cell to Golgi cell, and granule cell to basket cell synapses and exhibit a motor learning deficit at highest rotarod speeds. Since we detected Munc13-3 immunoreactivity in the dentate gyrus, as reported here for the first time, and current studies indicated a crucial role for the cerebellum in hippocampus-dependent spatial memory, we systematically investigated Munc13-3(−/−) mice versus wild-type littermates of both genders with respect to hippocampus-related cognition and a range of basic behaviors, including tests for anxiety, sensory functions, motor performance and balance, sensorimotor gating, social interaction and competence, and repetitive and compulsive behaviors. Neither basic behavior nor hippocampus-dependent cognitive performance, evaluated by Morris water maze, hole board working and reference memory, IntelliCage-based place learning including multiple reversals, and fear conditioning, showed any difference between genotypes. However, consistent with a disturbed cerebellar reflex circuitry, a reliable reduction in the acoustic startle response in both male and female Munc13-3(−/−) mice was found. To conclude, complete deletion of Munc13-3 leads to a robust decrease in the acoustic startle response. This readout of a fast cerebellar reflex circuitry obviously requires synaptic vesicle priming by Munc13-3 for full functionality, in contrast to other behavioral or cognitive features, where a nearly perfect compensation of Munc13-3 deficiency by related synaptic proteins has to be assumed

    Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations

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    Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. If based on current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems that are likely to exhibit quantum chaos. Here we describe a small, highly accurate quantum simulator and its use to run high fidelity simulations of three different model Hamiltonians for >100>100 time steps. While not scalable to exponentially large Hilbert spaces, this platform provides the accuracy and programmability required for systematic exploration of the interplay between dynamics, imperfections, and accuracy in quantum simulation.Comment: Published version. 10 pages, 5 figures, including Supplemental Materia
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