10,245 research outputs found
Continuous-variable quantum neural networks
We introduce a general method for building neural networks on quantum
computers. The quantum neural network is a variational quantum circuit built in
the continuous-variable (CV) architecture, which encodes quantum information in
continuous degrees of freedom such as the amplitudes of the electromagnetic
field. This circuit contains a layered structure of continuously parameterized
gates which is universal for CV quantum computation. Affine transformations and
nonlinear activation functions, two key elements in neural networks, are
enacted in the quantum network using Gaussian and non-Gaussian gates,
respectively. The non-Gaussian gates provide both the nonlinearity and the
universality of the model. Due to the structure of the CV model, the CV quantum
neural network can encode highly nonlinear transformations while remaining
completely unitary. We show how a classical network can be embedded into the
quantum formalism and propose quantum versions of various specialized model
such as convolutional, recurrent, and residual networks. Finally, we present
numerous modeling experiments built with the Strawberry Fields software
library. These experiments, including a classifier for fraud detection, a
network which generates Tetris images, and a hybrid classical-quantum
autoencoder, demonstrate the capability and adaptability of CV quantum neural
networks
The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
We investigate the role played by the vacuum of the primordial fluctuations
in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton
potential is a mass term and the unperturbed quantum geometry is governed by
the effective dynamics of Loop Quantum Cosmology. In this situation, the
phenomenologically interesting solutions have a preinflationary regime where
the kinetic energy of the inflaton dominates over the potential. For these kind
of solutions, we show that the primordial power spectra depend strongly on the
choice of vacuum. We study in detail the case of adiabatic states of low order
and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all
imposed at the bounce. The adiabatic spectra are typically suppressed at large
scales, and display rapid oscillations with an increase of power at
intermediate scales. In the non-oscillating vacuum, there is power suppression
for large scales, but the rapid oscillations are absent. We argue that the
oscillations are due to the imposition of initial adiabatic conditions in the
region of kinetic dominance, and that they would also be present in General
Relativity. Finally, we discuss the sensitivity of our results to changes of
the initial time and other data of the model.Comment: 29 pages, 13 figure
Fermions in Hybrid Loop Quantum Cosmology
This work pioneers the quantization of primordial fermion perturbations in
hybrid Loop Quantum Cosmology (LQC). We consider a Dirac field coupled to a
spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar
inflaton, and treat the Dirac field as a perturbation. We describe the
inhomogeneities of this field in terms of creation and annihilation variables,
chosen to admit a unitary evolution if the Dirac fermion were treated as a test
field. Considering instead the full system, we truncate its action at quadratic
perturbative order and construct a canonical formulation. In particular this
implies that, in the global Hamiltonian constraint of the model, the
contribution of the homogeneous sector is corrected with a quadratic
perturbative term. We then adopt the hybrid LQC approach to quantize the full
model, combining the loop representation of the homogeneous geometry with the
Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz
for physical states and show how to obtain a Schr\"odinger equation for the
quantum evolution of the perturbations, where the role of time is played by the
homogeneous inflaton. We prove that the resulting quantum evolution of the
Dirac field is indeed unitary, despite the fact that the underlying homogeneous
geometry has been quantized as well. Remarkably, in such evolution, the fermion
field couples to an infinite sequence of quantum moments of the homogeneous
geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is
shown to be an exact solution of the Schr\"odinger equation. Finally, we
discuss in detail the quantum backreaction that the fermion field introduces in
the global Hamiltonian constraint. For completeness, our quantum study includes
since the beginning (gauge-invariant) scalar and tensor perturbations, that
were studied in previous works.Comment: 29 pages. It matches published versio
Momentum maps for mixed states in quantum and classical mechanics
This paper presents the momentum map structures which emerge in the dynamics
of mixed states. Both quantum and classical mechanics are shown to possess
analogous momentum map pairs. In the quantum setting, the right leg of the pair
identifies the Berry curvature, while its left leg is shown to lead to more
general realizations of the density operator which have recently appeared in
quantum molecular dynamics. Finally, the paper shows how alternative
representations of both the density matrix and the classical density are
equivariant momentum maps generating new Clebsch representations for both
quantum and classical dynamics. Uhlmann's density matrix and Koopman-von
Neumann wavefunctions are shown to be special cases of this construction.Comment: 20 pages; no figures. To appear in J. Geom. Mec
Multiple Rabi Splittings under Ultra-Strong Vibrational Coupling
From the high vibrational dipolar strength offered by molecular liquids, we
demonstrate that a molecular vibration can be ultra-strongly coupled to
multiple IR cavity modes, with Rabi splittings reaching of the vibration
frequencies. As a proof of the ultra-strong coupling regime, our experimental
data unambiguously reveal the contributions to the polaritonic dynamics coming
from the anti-resonant terms in the interaction energy and from the dipolar
self-energy of the molecular vibrations themselves. In particular, we measure
the opening of a genuine vibrational polaritonic bandgap of ca. meV. We
also demonstrate that the multimode splitting effect defines a whole
vibrational ladder of heavy polaritonic states perfectly resolved. These
findings reveal the broad possibilities in the vibrational ultra-strong
coupling regime which impact both the optical and the molecular properties of
such coupled systems, in particular in the context of mode-selective chemistry.Comment: 10 pages, 9 figure
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