Quantum Poisson solver without arithmetic

Solving differential equations is one of the most promising applications of quantum computing. The Poisson equation has applications in various domains of physics and engineering, including the simulation of ocean current dynamics. Here, we propose an efficient quantum algorithm for solving the one-...

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Vydané v:Intelligent Marine Technology and Systems Ročník 2; číslo 1
Hlavní autori: Wang, Shengbin, Wang, Zhimin, Cui, Guolong, Shi, Shangshang, Shang, Ruimin, Li, Jiaxin, Li, Wendong, Wei, Zhiqiang, Gu, Yongjian
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Singapore Springer Nature Singapore 08.02.2024
Predmet:
Artificial Intelligence
Big Data
Computer Imaging
Earth and Environmental Science
Earth Sciences
Marine & Freshwater Sciences
Oceanography
Pattern Recognition and Graphics
Remote Sensing/Photogrammetry
Research Paper
Vision
Matrix diagonalization
Quantum linear systems algorithm
Poisson equation
Quantum arithmetic
ISSN:2948-1953, 2948-1953
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Popis
Shrnutí:Solving differential equations is one of the most promising applications of quantum computing. The Poisson equation has applications in various domains of physics and engineering, including the simulation of ocean current dynamics. Here, we propose an efficient quantum algorithm for solving the one-dimensional Poisson equation based on the controlled R y rotations. Our quantum Poisson solver (QPS) removes the need for expensive routines such as phase estimation, quantum arithmetic or Hamiltonian simulation. The computational cost of our QPS is 3 n in qubits and 5/3 n 3 in one- and two-qubit gates, where n is the logarithmic of the number of discrete points. An overwhelming reduction of the constant factors of the big-O complexity is achieved, which is critical to evaluate the practicality of implementing the algorithm on a quantum computer. In terms of the error ε , the complexity is log(1/ ε ) in qubits and poly(log(1/ ε )) in operations. The algorithms are demonstrated using a quantum virtual computing system, and the circuits are executed successfully on the IBM real quantum computers. The present QPS could exhibit a potential real-world application for solving differential equations on noisy intermediate-scale quantum (NISQ) devices.
ISSN:2948-1953
2948-1953
DOI:10.1007/s44295-023-00020-1