Related papers: Solving the Schrodinger equation with genetic algo…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a…
The purpose of this paper is to present a method of solving the Shr\"odinger Equation (SE) by Genetic Algorithms and Grammatical Evolution. The method forms generations of trial solutions expressed in an analytical form. We illustrate the…
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schr\"odinger equation for realistic molecules and materials but is characterized by an unfavourable scaling, which strongly limits its…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum…
Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
A derivation of stochastic Schrodinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the…
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge…
Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…
In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials,…
The belief propagation algorithm has been recognized in the information theory community as a soft-decision iterative decoding algorithm. It is the most powerful algorithm found so far for attacking hard optimization problems in channel…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…
Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…