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We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
The methodology based on the association of the Variational Method with Supersymmetric Quantum Mechanics is used to evaluate the energy states of the confined hydrogen atom.
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
A new scheme of field quantization is proposed. Instead of associating with different frequencies different oscillators we begin with a single oscillator that can exist in a superposition of different frequencies. The idea is applied to the…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous…
Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the…
The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is…
We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
Rapid advances are being made toward optically cooling a single mode of a micro-mechanical system to its quantum ground state and observing quantum behavior at macroscopic scales. Reaching this regime in room-temperature environments…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing…
An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum…
The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a…
We study L\'evy flights confined in a parabolic potential. This has to do with a fractional generalization of ordinary quantum-mechanical oscillator problem. To solve the spectral problem for the fractional quantum oscillator, we pass to…