2,317 research outputs found
Characterizing dynamics with covariant Lyapunov vectors
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
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 -body collective interaction (or -order
twisting), beyond the usual case of . Using our geometric framework, we
prove a no-go theorem for the local optimality of these models for .Comment: 15 pages, 6 figures, 9 pages appendi
Simulation of complex dynamics of mean-field -spin models using measurement-based quantum feedback control
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 -spin Hamiltonians, which describe Ising-like models on a
completely connected graph with -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 -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 . 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
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
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
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
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(â/â)) 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(â/â) 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(â/â) 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
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 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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