2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 2022
DOI: 10.1109/qce53715.2022.00146
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Solving Partial Differential Equations using a Quantum Computer

Abstract: The simulation of quantum systems currently constitutes one of the most promising applications of quantum computers. However, the integration of more general partial differential equations (PDEs) for models of classical systems that are not governed by the laws of quantum mechanics remains a fundamental challenge. Current approaches such as the Variational Quantum Linear Solver (VQLS) method can accumulate large errors and the associated quantum circuits are difficult to optimize. A recent method based on the … Show more

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Cited by 4 publications
(3 citation statements)
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“…a polynomial number of steps) but can be verified in a polynomial time given their solutions, and NPhard problems are computational problems harder than NP problems. On the other hand, quantum machines harnessing quantum physics phenomena like entanglement can solve some challenging problems faster and more efficiently than their counterpart conventional machines ranging from integer optimization problems [11]- [13] to AI techniques [14]- [18] and PDEs, [19], [20], and even quantum-inspired algorithms for solving PDEs [21]. Thus, quantum algorithms' computational advantages (or quantum advantage) over conventional algorithms inspire enough to examine and identify computationally intractable problems with EO methodologies and hard EO datasets for near-and far-term quantum machines.…”
Section: A Why Quantum Computing For Earth Observation?mentioning
confidence: 99%
“…a polynomial number of steps) but can be verified in a polynomial time given their solutions, and NPhard problems are computational problems harder than NP problems. On the other hand, quantum machines harnessing quantum physics phenomena like entanglement can solve some challenging problems faster and more efficiently than their counterpart conventional machines ranging from integer optimization problems [11]- [13] to AI techniques [14]- [18] and PDEs, [19], [20], and even quantum-inspired algorithms for solving PDEs [21]. Thus, quantum algorithms' computational advantages (or quantum advantage) over conventional algorithms inspire enough to examine and identify computationally intractable problems with EO methodologies and hard EO datasets for near-and far-term quantum machines.…”
Section: A Why Quantum Computing For Earth Observation?mentioning
confidence: 99%
“…a polynomial number of steps) but can be verified in a polynomial time given their solutions, and NP-hard problems are computational problems harder than NP problems. Furthermore, quantum machines harnessing quantum physics phenomena like entanglement can solve some hard problems faster and more efficiently than their counterpart conventional machines ranging from integer optimization problems [11]- [13] to AI techniques [14]- [18] and to PDEs [19], [20], and even quantum-inspired algorithms for solving PDEs [21]. These computational advantages of quantum algorithms (or quantum advantage) over conventional algorithms inspire enough to examine and identify computationally intractable problems with EO methodologies as well as hard EO datasets for near-and far-term quantum machines.…”
Section: A Why Quantum Computing For Earth Observation?mentioning
confidence: 99%
“…Partial differential equations (PDEs) are fundamental to solving important problems in engineering and science. With the advent of nascent quantum computers, finding new efficient quantum algorithms and hardware for solving PDEs has become an active area of research (Tosti Balducci et al , 2022; Jin et al , 2022; Leong et al , 2022; Pool et al , 2022) in disciplines ranging from fluid dynamics (Budinski, 2021; Gaitan, 2020; Steijl, 2022; Steijl and Barakos, 2018; Griffin et al , 2019; Li et al , 2023), heat conduction (Liu et al , 2022) and electromagnetics (Ewe et al , 2022) to quantitative finance (Fontanela et al , 2021) and cosmology (Mocz and Szasz, 2021).…”
Section: Introductionmentioning
confidence: 99%