Solving the Schrödinger equation using program synthesis
- 15 October 2021
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 155 (15), 154102
- https://doi.org/10.1063/5.0062497
Abstract
We demonstrate that a program synthesis approach based on a linear code representation can be used to generate algorithms that approximate the ground-state solutions of one-dimensional time-independent Schrödinger equations constructed with bound polynomial potential energy surfaces (PESs). Here, an algorithm is constructed as a linear series of instructions operating on a set of input vectors, matrices, and constants that define the problem characteristics, such as the PES. Discrete optimization is performed using simulated annealing in order to identify sequences of code-lines, operating on the program inputs that can reproduce the expected ground-state wavefunctions ψ(x) for a set of target PESs. The outcome of this optimization is not simply a mathematical function approximating ψ(x) but is, instead, a complete algorithm that converts the input vectors describing the system into a ground-state solution of the Schrödinger equation. These initial results point the way toward an alternative route for developing novel algorithms for quantum chemistry applications.This publication has 58 references indexed in Scilit:
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