A wavelet-based Projector Augmented-Wave (PAW) method: reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set

We present a Projector Augmented-Wave~(PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order-N simulations within a PAW method

QPROP: A Schroedinger-solver for intense laser-atom interaction

The Qprop package is presented. Qprop has been developed to study laser-atom interaction in the nonperturbative regime where nonlinear phenomena such as above-threshold ionization, high order harmonic generation, and dynamic stabilization are known to occur. In the nonrelativistic regime and within the single active electron approximation, these phenomena can be studied with Qprop in the most rigorous way by solving the time-dependent Schr\"odinger equation in three spatial dimensions. Because Qprop is optimized for the study of quantum systems that are spherically symmetric in their initial, unperturbed configuration, all wavefunctions are expanded in spherical harmonics. Time-propagation of the wavefunctions is performed using a split-operator approach. Photoelectron spectra are calculated employing a window-operator technique. Besides the solution of the time-dependent Schr\"odinger equation in single active electron approximation, Qprop allows to study many-electron systems via the solution of the time-dependent Kohn-Sham equations.Comment: 40 pages, LaTeX; to obtain the QPROP source code visit http://www.qprop.de, accepted for publication in Computer Physics Communication

Biexciton stability in carbon nanotubes

We have applied the quantum Monte Carlo method and tight-binding modelling to calculate the binding energy of biexcitons in semiconductor carbon nanotubes for a wide range of diameters and chiralities. For typical nanotube diameters we find that biexciton binding energies are much larger than previously predicted from variational methods, which easily brings the biexciton binding energy above the room temperature threshold.Comment: revtex4, final, twocolumn. to be published in Phys.Rev.Let. 5 pages 3 figure

Spin coherent quantum transport of electrons between defects in diamond

The nitrogen-vacancy color center in diamond has rapidly emerged as an important solid-state system for quantum information processing. While individual spin registers have been used to implement small-scale diamond quantum computing, the realization of a large-scale device requires development of an on-chip quantum bus for transporting information between distant qubits. Here we propose a method for coherent quantum transport of an electron and its spin state between distant NV centers. Transport is achieved by the implementation of spatial stimulated adiabatic Raman passage through the optical control of the NV center charge states and the confined conduction states of a diamond nanostructure. Our models show that for two NV centers in a diamond nanowire, high fidelity transport can be achieved over distances of order hundreds of nanometres in timescales of order hundreds of nanoseconds. Spatial adiabatic passage is therefore a promising option for realizing an on-chip spin quantum bus

Solution of Schrödinger Equation for Quantum Systems via Physics-Informed Neural Networks

openThe numerous successes achieved by machine learning techniques in many technical areas have sparked interest in the scientific community for their application in science. By merging the knowledge of machine learning experts and computational scientists, the field of scientific machine learning has shown its ability to greatly improve the performance of existing computational methods. One possible approach to developing physics-aware machine learning is the inclusion of physical constraints in the training of a machine learning model. Physics-Informed Neural Networks are an example of such an approach, as they can incorporate prior physical knowledge into their architecture, enabling them to learn and simulate complex phenomena while respecting the underlying physics principles. Possible constraints are physical laws, symmetries, and conservation laws. Compared to other machine learning models, Physics-Informed Neural Networks do not require substantial input data, with the exception of initial and boundary conditions to correctly formalize the problem. In this Thesis, we exploit the advantages of Physics-Informed Neural Networks to efficiently simulate one-electron quantum systems. The simulations rely on the direct solution of the eigenvalue equation represented by the Schrödinger equation. Traditional methods for solving the Schrödinger equation often rely on approximations and can become computationally expensive for nontrivial systems. The mesh-free Physics-Informed Neural Networks approach avoids the need for discretization, as the residuals computed with respect to the physical constraints are minimized during training for a given set of points within the domain. The solution of the Schrödinger equation allows one to calculate important physical quantities of the physical system under study, such as the ground state energy, the electronic wavefunction, and the associated electron density. These quantities are compared with the estimations present in the quantum chemistry literature to assess the performance of the Physics-Informed Machine Learning approach.The numerous successes achieved by machine learning techniques in many technical areas have sparked interest in the scientific community for their application in science. By merging the knowledge of machine learning experts and computational scientists, the field of scientific machine learning has shown its ability to greatly improve the performance of existing computational methods. One possible approach to developing physics-aware machine learning is the inclusion of physical constraints in the training of a machine learning model. Physics-Informed Neural Networks are an example of such an approach, as they can incorporate prior physical knowledge into their architecture, enabling them to learn and simulate complex phenomena while respecting the underlying physics principles. Possible constraints are physical laws, symmetries, and conservation laws. Compared to other machine learning models, Physics-Informed Neural Networks do not require substantial input data, with the exception of initial and boundary conditions to correctly formalize the problem. In this Thesis, we exploit the advantages of Physics-Informed Neural Networks to efficiently simulate one-electron quantum systems. The simulations rely on the direct solution of the eigenvalue equation represented by the Schrödinger equation. Traditional methods for solving the Schrödinger equation often rely on approximations and can become computationally expensive for nontrivial systems. The mesh-free Physics-Informed Neural Networks approach avoids the need for discretization, as the residuals computed with respect to the physical constraints are minimized during training for a given set of points within the domain. The solution of the Schrödinger equation allows one to calculate important physical quantities of the physical system under study, such as the ground state energy, the electronic wavefunction, and the associated electron density. These quantities are compared with the estimations present in the quantum chemistry literature to assess the performance of the Physics-Informed Machine Learning approach

Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions

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, but only at large computational cost. Whereas in many domains models are trained once and subsequently applied for inference, accurate DL-VMC so far requires a full optimization for every new problem instance, consuming thousands of GPUhs even for small molecules. We instead propose a DL-VMC model which has been pre-trained using self-supervised wavefunction optimization on a large and chemically diverse set of molecules. Applying this model to new molecules without any optimization, yields wavefunctions and absolute energies that outperform established methods such as CCSD(T)-2Z. To obtain accurate relative energies, only few fine-tuning steps of this base model are required. We accomplish this with a fully end-to-end machine-learned model, consisting of an improved geometry embedding architecture and an existing SE(3)-equivariant model to represent molecular orbitals. Combining this architecture with continuous sampling of geometries, we improve zero-shot accuracy by two orders of magnitude compared to the state of the art. We extensively evaluate the accuracy, scalability and limitations of our base model on a wide variety of test systems