Related papers: Solving the Schrodinger equation with genetic algo…
A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most…
Stochastic Schr\"odinger equations that govern the dynamics of open quantum systems are given by the equations for signal processing. In particular, the Brownian motion that drives the wave function of the system does not represent noise,…
B-spline collocation techniques have been applied to Schr\"odinger's equation since the early 1970s, but one aspect that is noticeably missing from this literature is the use of Gaussian points (i.e., the zeros of Legendre polynomials) as…
Challenges in natural sciences can often be phrased as optimization problems. Machine learning techniques have recently been applied to solve such problems. One example in chemistry is the design of tailor-made organic materials and…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the…
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
Hylleraas in 1929 carried out a variational computation on the Schrodinger equation for the helium atom which gave, for the first time, a ground-state energy in essential agreement with experimental results. Coolidge and James in 1933,…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
A new approach to the steering problem for quantum systems relying on Nelson's stochastic mechanics and on the theory of Schroedinger bridges is presented. The method is illustrated by working out a simple Gaussian example.
Designing efficient quantum circuits that leverage quantum advantage compared to classical computing has become increasingly critical. Genetic algorithms have shown potential in generating such circuits through artificial evolution.…
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
In return for the long-standing contributions of Physics to Biology, now the inverse way is frequently traveled through in order to think about many physics phenomena. In this vein, evolutionary algorithms, particularly genetic algorithms,…