Quantum Fourier networks for solving parametric PDEs Article Swipe
Nishant Jain
,
Jonas Landman
,
Natansh Mathur
,
Iordanis Kerenidis
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1088/2058-9565/ad42ce
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1088/2058-9565/ad42ce
Many real-world problems, like modelling environment dynamics, physical processes, time series etc involve solving partial differential equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture called Fourier neural operator (FNO) proved to be capable of learning solutions of given PDE families for any initial conditions as input. However, it results in a time complexity linear in the number of evaluations of the PDEs while testing. Given the advancements in quantum hardware and the recent results in quantum machine learning methods, we exploit the running efficiency offered by these and propose quantum algorithms inspired by the classical FNO, which result in time complexity logarithmic in the number of evaluations and are expected to be substantially faster than their classical counterpart. At their core, we use the unary encoding paradigm and orthogonal quantum layers and introduce a new quantum Fourier transform in the unary basis. We propose three different quantum circuits to perform a quantum FNO. The proposals differ in their depth and their similarity to the classical FNO. We also benchmark our proposed algorithms on three PDE families, namely Burgers’ equation, Darcy’s flow equation and the Navier–Stokes equation. The results show that our quantum methods are comparable in performance to the classical FNO. We also perform an analysis on small-scale image classification tasks where our proposed algorithms are at par with the performance of classical convolutional neural networks, proving their applicability to other domains as well.
Related Topics
Concepts
Partial differential equation
Quantum algorithm
Quantum
Algorithm
Computer science
Quantum Fourier transform
Mathematics
Applied mathematics
Mathematical optimization
Quantum gate
Mathematical analysis
Physics
Quantum mechanics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1088/2058-9565/ad42ce
- OA Status
- hybrid
- Cited By
- 8
- References
- 48
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https://doi.org/10.1088/2058-9565/ad42ceDigital Object Identifier
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Quantum Fourier networks for solving parametric PDEsWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-04-24Full publication date if available
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Nishant Jain, Jonas Landman, Natansh Mathur, Iordanis KerenidisList of authors in order
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https://doi.org/10.1088/2058-9565/ad42cePublisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1088/2058-9565/ad42ceDirect OA link when available
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Partial differential equation, Quantum algorithm, Quantum, Algorithm, Computer science, Quantum Fourier transform, Mathematics, Applied mathematics, Mathematical optimization, Quantum gate, Mathematical analysis, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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8Total citation count in OpenAlex
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2025: 8Per-year citation counts (last 5 years)
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| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Quantum Science and Technology |
| primary_location.landing_page_url | https://doi.org/10.1088/2058-9565/ad42ce |
| publication_date | 2024-04-24 |
| publication_year | 2024 |
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