Two quantum algorithms for solving the one-dimensional advection-diffusion equation Article Swipe
Julia Ingelmann
,
Sachin S. Bharadwaj
,
Philipp Pfeffer
,
Katepalli R. Sreenivasan
,
Jörg Schumacher
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.00326
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.00326
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithms (QLSA) based on the Harrow--Hassidim--Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to $N=64$ grid points on the unit interval. Both algorithms are of hybrid nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the sizes of an additional quantum register for the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement and decoherence circuit noise. We reflect the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.
Related Topics
Concepts
Quantum algorithm
Quantum phase estimation algorithm
Algorithm
Quantum computer
Qubit
Computer science
Solver
Mathematics
Quantum
Applied mathematics
Quantum error correction
Mathematical optimization
Quantum mechanics
Physics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.00326
- https://arxiv.org/pdf/2401.00326
- OA Status
- green
- References
- 47
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4390528642Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2401.00326Digital Object Identifier
- Title
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Two quantum algorithms for solving the one-dimensional advection-diffusion equationWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-12-30Full publication date if available
- Authors
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Julia Ingelmann, Sachin S. Bharadwaj, Philipp Pfeffer, Katepalli R. Sreenivasan, Jörg SchumacherList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.00326Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2401.00326Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2401.00326Direct OA link when available
- Concepts
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Quantum algorithm, Quantum phase estimation algorithm, Algorithm, Quantum computer, Qubit, Computer science, Solver, Mathematics, Quantum, Applied mathematics, Quantum error correction, Mathematical optimization, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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