2026-10-14T02:46:04Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33839728 2026-09-16T10:17:48Z portal_1197 item_type_3 month_year_09_2026

Data for Program synthesis of sparse algorithms for wave function and energy prediction in grid-based quantum simulations Scott Habershon (1263891) Wave functions Potential energy surfaces Quantum chemistry Hamiltonian systems Automatic programming (Computer science) Neural networks (Computer science) Migrated from ePrints We have recently shown how program synthesis (PS), or the concept of ``self-writing code'', can generate novel algorithms that solve the vibrational Schrodinger equation, providing approximations to the allowed wavefunctions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wavefunction \psi(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wavefunctions and energy eigenvalues of representative model PESs (both 1-D and multi-dimensional). We show that PS can generate algorithms which offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods which exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multi-dimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order-of-magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wavefunction propagation, and evaluation of molecular electronic structure.<br><br>This directory contains datasets from Figs. 2-6 in Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid Based Quantum Simulations. Each directory contains standard ascii text files. 2022-03-15T00:00:00Z Dataset Dataset 10.82444/warw.33839728.v1 https://figshare.com/articles/dataset/Data_for_Program_synthesis_of_sparse_algorithms_for_wave_function_and_energy_prediction_in_grid-based_quantum_simulations/33839728 CC BY 4.0