Quantum Spectral Methods for Differential Equations
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Available literature reveals the application of quantum algorithms to solve linear and differential equations, where these algorithms play the role of subroutines in algorithms on data processing.
“Available pieces of literature reveal the application of quantum algorithms to solve linear [75] and differential equations [76-78], where these algorithms play the role of 'subroutines' in algorithms on data processing.”
From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [78]
The Introduction (pp. 1–2) describes quantum algorithms for differential equations built on a quantum linear-systems algorithm, and the Discussion (p. 22) says this paper presents an algorithm for linear ODEs. It does not establish the further claim that equation-solving algorithms serve as subroutines in data-processing algorithms. The subroutines mentioned in the Introduction (p. 3) instead provide inputs to this paper’s algorithm. (LLM, conf=0.85)
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References 49 · Cited by 133
Research works printed but not linked: 21
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- [3][3] Juan Miguel Arrazola, Timjan Kalajdzievski, Christian Weedbrook, and Seth Lloyd, Quantum algorithm for non-homogeneous linear partial differential equations , arXiv:1809.02622. - · arXiv
- [4][4] Esmail Babolian and Mohammad Mahdi Hosseini, A modified spectral method for numerical solution of ordinary differential equations with non-analytic solution , Applied Mathematics and Computation (2002), 132(2), 341-351. -
- [7][7] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma, Exponential improvement in precision for simulating sparse Hamiltonians , Proceedings of the 46th Annual ACM Symposium on Theory of Computing (2014), pp. 283-292, arXiv:1312.1414. - · arXiv
- [8][8] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma, Simulating Hamiltonian dynamics with a truncated Taylor series , Physical Review Letters (2015), 114, no. 9, 090502, arXiv:1412.4687. - · arXiv
- [9][9] Dominic W. Berry, Andrew M. Childs, and Robin Kothari, Hamiltonian simulation with nearly optimal dependence on all parameters , Proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science (2015), pp. 792-809, arXiv:1501.01715. - · arXiv
- [10][10] Dominic W. Berry, Andrew M. Childs, Aaron Ostrander, Guoming Wang, Quantum algorithm for linear differential equations with exponentially improved dependence on precision , Communications in Mathematical Physics (2017), 356, no. 3, 1057-1081, arXiv:1701.03684. - · arXiv
- [11][11] Dominic W. Berry and Leonardo Novo, Corrected quantum walk for optimal Hamiltonian simulation , Quantum Information and Computation (2016), 16, no. 15-16, 1295, arXiv:1606.03443. - · arXiv
- [15][15] Andrew M. Childs, Robin Kothari, and Rolando D. Somma, Quantum linear systems algorithm with exponentially improved dependence on precision , SIAM Journal on Computing (2017), 46, 1920-1950, arXiv:1511.02306. - · arXiv
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- Authors
- Childs, A. M., & Liu, J.-P.
- Affiliations
- Joint Center for Quantum Information and Computer Science (US)
- Corresponding author
- Liu, Jin-Peng
- Venue
- Communications in Mathematical Physics
- Published
- 2020-02-18
- Volume
- 375
- Issue
- 2
- Pages
- 1427-1457
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2908285344
- Cited by
- 133
- References
- 49
- Citations by year
- 2026: 11 · 2025: 31 · 2024: 31 · 2023: 25 · 2022: 21 · 2021: 9 · 2020: 4
- FWCI
- 5.70
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Communications in Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Army Research Office (MURI award W911NF-16-1-0349)
- Canadian Institute for Advanced Research
- National Science Foundation (1526380, 1813814)
- U.S. Department of Energy Quantum Algorithms Teams
- U.S. Department of Energy Quantum Testbed Pathfinder (DE-SC0019040)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum algorithms, spectral methods, linear ordinary differential equations, time-dependent coefficients, initial value problems, boundary value problems, quantum linear systems, numerical solution of differential equations
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