Related papers: Superiority of semiclassical over quantum mechanic…
The N-dimensional generalization of Bertrand spaces as families of Maximally superintegrable systems on spaces with nonconstant curvature is analyzed. Considering the classification of two dimensional radial systems admitting 3 constants of…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…
It has been long recognized that the task of semiclassical evaluation of quantum spectra for the classically nonintegrable systems is fundamentally more complex than for the classically integrable ones. Below it is argued that the quantum…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe classical phenomena. Not only are the…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
We study the semiclassical behaviour of a two--dimensional nonintegrable system. In particular we analyze the question of quantum corrections to the semiclassical quantization obtaining up to the second order of perturbation theory an…
The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For…
We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
The semi-classical solution of the three state system is considered to study the population inversion at and away from resonance. At resonance, it is shown that if the system is initially populated either in the upper or in the lower level,…