21,324 research outputs found
Data-driven Efficient Solvers and Predictions of Conformational Transitions for Langevin Dynamics on Manifold in High Dimensions
We work on dynamic problems with collected data that
distributed on a manifold . Through the
diffusion map, we first learn the reaction coordinates where is a manifold isometrically embedded into an
Euclidean space for . The reaction coordinates
enable us to obtain an efficient approximation for the dynamics described by a
Fokker-Planck equation on the manifold . By using the reaction
coordinates, we propose an implementable, unconditionally stable, data-driven
upwind scheme which automatically incorporates the manifold structure of
. Furthermore, we provide a weighted convergence analysis of
the upwind scheme to the Fokker-Planck equation. The proposed upwind scheme
leads to a Markov chain with transition probability between the nearest
neighbor points. We can benefit from such property to directly conduct
manifold-related computations such as finding the optimal coarse-grained
network and the minimal energy path that represents chemical reactions or
conformational changes. To establish the Fokker-Planck equation, we need to
acquire information about the equilibrium potential of the physical system on
. Hence, we apply a Gaussian Process regression algorithm to
generate equilibrium potential for a new physical system with new parameters.
Combining with the proposed upwind scheme, we can calculate the trajectory of
the Fokker-Planck equation on based on the generated equilibrium
potential. Finally, we develop an algorithm to pullback the trajectory to the
original high dimensional space as a generative data for the new physical
system.Comment: 59 pages, 16 figure
Experimentally reducing the quantum measurement back-action in work distributions by a collective measurement
In quantum thermodynamics, the standard approach to estimate work
fluctuations in unitary processes is based on two projective measurements, one
performed at the beginning of the process and one at the end. The first
measurement destroys any initial coherence in the energy basis, thus preventing
later interference effects. In order to decrease this back-action, a scheme
based on collective measurements has been proposed in~[PRL 118, 070601 (2017)].
Here, we report its experimental implementation in an optical system. The
experiment consists of a deterministic collective measurement on identically
prepared two qubits, encoded in the polarisation and path degree of a single
photon. The standard two projective measurement approach is also experimentally
realized for comparison. Our results show the potential of collective schemes
to decrease the back-action of projective measurements, and capture subtle
effects arising from quantum coherence.Comment: 9 pages, 4 figure
Building quantum neural networks based on swap test
Artificial neural network, consisting of many neurons in different layers, is
an important method to simulate humain brain. Usually, one neuron has two
operations: one is linear, the other is nonlinear. The linear operation is
inner product and the nonlinear operation is represented by an activation
function. In this work, we introduce a kind of quantum neuron whose inputs and
outputs are quantum states. The inner product and activation operator of the
quantum neurons can be realized by quantum circuits. Based on the quantum
neuron, we propose a model of quantum neural network in which the weights
between neurons are all quantum states. We also construct a quantum circuit to
realize this quantum neural network model. A learning algorithm is proposed
meanwhile. We show the validity of learning algorithm theoretically and
demonstrate the potential of the quantum neural network numerically.Comment: 10 pages, 13 figure
Orientation and Motion of Water Molecules at Air/Water Interface
Analysis of SFG vibrational spectra of OH stretching bands in four
experimental configurations shows that orientational motion of water molecule
at air/water interface is libratory within a limited angular range. This
picture is significantly different from the previous conclusion that the
interfacial water molecule orientation varies over a broad range within the
vibrational relaxation time, the only direct experimental evidence for
ultrafast and broad orientational motion of a liquid interface by Wei et al.
[Phys. Rev. Lett. 86, 4799, (2001)] using single SFG experimental
configuration
Rapidity bin multiplicity correlations from a multi-phase transport model
The central-arbitrary bin and forward-backward bin multiplicity correlation
patterns for Au+Au collisions at = GeV are
investigated within a multi-phase transport (AMPT) model. An interesting
observation is that for GeV Au+Au collisions, these two
correlation patterns both have an increase with the pseudorapidity gap, while
for GeV Au+Au collisions, they decrease. We mainly
discuss the influence of different evolution stages of collision system on the
central-arbitrary bin correlations, such as the initial conditions, partonic
scatterings, hadronization scheme and hadronic scatterings. Our results show
that the central-arbitrary bin multiplicity correlations have different
responses to partonic phase and hadronic phase, which can be suggested as a
good probe to explore the dynamical evolution mechanism of the hot dense matter
in high-energy heavy-ion collisions.Comment: 7pages, 6 figures, accepted for publication in EPJ
Deterministic realization of collective measurements via photonic quantum walks
Collective measurements on identically prepared quantum systems can extract
more information than local measurements, thereby enhancing
information-processing efficiency. Although this nonclassical phenomenon has
been known for two decades, it has remained a challenging task to demonstrate
the advantage of collective measurements in experiments. Here we introduce a
general recipe for performing deterministic collective measurements on two
identically prepared qubits based on quantum walks. Using photonic quantum
walks, we realize experimentally an optimized collective measurement with
fidelity 0.9946 without post selection. As an application, we achieve the
highest tomographic efficiency in qubit state tomography to date. Our work
offers an effective recipe for beating the precision limit of local
measurements in quantum state tomography and metrology. In addition, our study
opens an avenue for harvesting the power of collective measurements in quantum
information processing and for exploring the intriguing physics behind this
power.Comment: Close to the published versio
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