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Kumar, S. and Wilmott, C.M., 2024. Generalising quantum imaginary time evolution to solve linear partial differential equations. Scientific Reports, 14: 20156. ISSN 2045-2322
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Abstract
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate ground states of various physical systems. In this paper, we demonstrate a practical application of QITE as a quantum numerical solver for linear partial differential equations. Our algorithm takes inspiration from QITE in that the quantum state follows the same normalised trajectory in both algorithms. However, it is our QITE methodology’s ability to track the scale of the state vector over time that allows our algorithm to solve differential equations. We demonstrate our methodology with numerical simulations and use it to solve the heat equation in one and two dimensions using six and ten qubits, respectively.
| Item Type: | Journal article | ||||||
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| Publication Title: | Scientific Reports | ||||||
| Creators: | Kumar, S. and Wilmott, C.M. | ||||||
| Publisher: | Springer Science and Business Media LLC | ||||||
| Date: | 2024 | ||||||
| Volume: | 14 | ||||||
| ISSN: | 2045-2322 | ||||||
| Identifiers: |
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| Rights: | © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. | ||||||
| Divisions: | Schools > School of Science and Technology | ||||||
| Record created by: | Melissa Cornwell | ||||||
| Date Added: | 01 Oct 2024 14:53 | ||||||
| Last Modified: | 01 Oct 2024 14:53 | ||||||
| URI: | https://irep.ntu.ac.uk/id/eprint/52336 |
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