Related papers: Solving the Schr\"odinger Equation in the Configur…
In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…
While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in…
Although machine learning has been successfully used to propose novel molecules that satisfy desired properties, it is still challenging to explore a large chemical space efficiently. In this paper, we present a conditional molecular design…
The concept of machine learning configuration interaction (MLCI) [J. Chem. Theory Comput. 2018, 14, 5739], where an artificial neural network (ANN) learns on the fly to select important configurations, is further developed so that accurate…
Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…
Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…
At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
In this paper, we propose a quantum algorithm that combines the momentum accelerated gradient method with Schr\"odingerization [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024), 230602][S. Jin, N. Liu and Y. Yu, Phys. Rev. A, 108…
Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
Accurate solution of the many-electron problem including correlations remains intractable except for few-electron systems. Describing interacting electrons as a superposition of independent electron configurations results in an apparent…
We consider the nonlinear Schr\"odinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss of…
Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
We propose an approach to generative quantum machine learning that overcomes the fundamental scaling issues of variational quantum circuits. The core idea is to use a class of generative models based on instantaneous quantum polynomial…
We outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we showed that the effective potential can be probabilistically…
This article presents an approach to the two-dimensional Schr\"odinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential,…