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Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to…
In this work we explain the relevance of the Differential Galois Theory in the semiclassical (or WKB) quantification of some two degree of freedom potentials. The key point is that the semiclassical path integral quantification around a…
The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead…
The classical WKB method (also known as the WKBJ method, the LG method, or the phase integral method) for solving singularly perturbed linear differential equations has never, as far as we know, been looked at from the structured backward…
The possibility of using the generator coordinate method (GCM) using hybrid quantum-classical algorithms with reduced quantum resources is discussed. The task of preparing the basis states and calculating the various kernels involved in the…
Structure-based virtual screening must address a combinatorial explosion arising from up to 10^60 drug-like molecules, multiple conformations of proteins and ligands, and all possible spatial translations and rotations of ligands within the…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat…
This paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
In this work, we show an application of the de Broglie-Bohm Quantum Theory of Motion (QTM) as a powerful tool for evaluating Bohm's quantum force in the scattering process of a Gaussian wavepacket by a classical Eckart potential. Our…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
A kinetic theory for quantum Langmuir waves interacting nonlinearly with quantum ion-acoustic waves is derived. The formulation allows for a statistical analysis of the quantum correction to the Zakharov system. The influence of a…
The Mittag-Leffler type functions arise naturally in the solution of fractional order integral and differential equations, especially in the investigations of the fractional generalization of the kinetic equation. This article introduces a…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQA), are suitable for implementation on NISQ computers. In this Letter we expand an implicit step of VQAs: the classical pre-computation subroutine which can…