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Solving the Schrödinger equation using program synthesis
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Habershon, Scott (2021) Solving the Schrödinger equation using program synthesis. Journal of Chemical Physics, 155 . 154102. doi:10.1063/5.0062497 ISSN 0021-9606.
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Official URL: 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 which 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 which define the problem characteristics, such as the PES. Discrete optimization is performed using sim- ulated annealing in order to identify sequences of code-lines, operating on the program inputs, which 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 ap- proximating ψ(x), but is instead a complete algorithm which converts the input vectors describing the system into a ground-state solution of the Schrödinger equation. These ini- tial results point the way towards an alternative route for developing novel algorithms for quantum chemistry applications.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QD Chemistry | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Chemistry Faculty of Science, Engineering and Medicine > Science > Chemistry > Computational and Theoretical Chemistry Centre |
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Library of Congress Subject Headings (LCSH): | Quantum chemistry, Schrödinger equation, Electronic structure -- Mathematical models, Quantum computing | ||||||||
Journal or Publication Title: | Journal of Chemical Physics | ||||||||
Publisher: | American Institute of Physics | ||||||||
ISSN: | 0021-9606 | ||||||||
Official Date: | 2021 | ||||||||
Dates: |
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Volume: | 155 | ||||||||
Article Number: | 154102 | ||||||||
DOI: | 10.1063/5.0062497 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Habershon, Scott (2021) Solving the Schrödinger equation using program synthesis. Journal of Chemical Physics, 155. 154102. and may be found at https://doi.org/10.1063/5.0062497 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 24 November 2021 | ||||||||
Date of first compliant Open Access: | 26 November 2021 |
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