Related papers: Affine Quantization on the Half Line
Quantum interferometry methods exploit quantum resources, such as photonic entanglement, to enhance phase estimation beyond classical limits. Nonlinear optics has served as a workhorse for the generation of entangled photon pairs, ensuring…
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
To quantify single mode nonclassicality, we start from an operational approach. A positive semi-definite observable is introduced to describe a measurement setup. The quantification is based on the negativity of the normally ordered version…
Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
We develop a systematic classical framework to accommodate canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
In some instances of study of quantum evolution of classical backgrounds it is considered inevitable to resort to non-perturbative methods at the price of treating the system semiclassically. We show that a fully quantum perturbative…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…
We study a fluid of quantum hard-spheres treated with affine-quantization. Assuming that the fluid obeys to Bose-Einstein statistics we solve for its thermodynamic properties using the path integral Monte Carlo method.
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could…
A general procedure for construction of the formalism of quantum beam optics for any particle is reviewed. The quantum formalism of spin-1/2 particle beam optics is presented starting {\em ab initio} with the Dirac equation. As an example…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
We consider a range of unconventional modifications to Quantum Annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by "transverse field chaos" in larger systems, classical…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…