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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| Vydáno v: | Intelligent Marine Technology and Systems Ročník 2; číslo 1 |
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Springer Nature Singapore
08.02.2024
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| ArticleNumber | 3 |
| Author | Li, Wendong Wang, Zhimin Shi, Shangshang Wei, Zhiqiang Wang, Shengbin Shang, Ruimin Li, Jiaxin Gu, Yongjian Cui, Guolong |
| Author_xml | – sequence: 1 givenname: Shengbin surname: Wang fullname: Wang, Shengbin organization: Faculty of Information Science and Engineering, Ocean University of China, Origin Quantum Computing Company Limited – sequence: 2 givenname: Zhimin orcidid: 0000-0001-9758-4388 surname: Wang fullname: Wang, Zhimin email: wangzhimin@ouc.edu.cn organization: Faculty of Information Science and Engineering, Ocean University of China – sequence: 3 givenname: Guolong surname: Cui fullname: Cui, Guolong organization: Faculty of Information Science and Engineering, Ocean University of China, Beijing Zhongke Arclight Quantum Software Technology Co., Ltd – sequence: 4 givenname: Shangshang surname: Shi fullname: Shi, Shangshang organization: Faculty of Information Science and Engineering, Ocean University of China – sequence: 5 givenname: Ruimin surname: Shang fullname: Shang, Ruimin organization: Faculty of Information Science and Engineering, Ocean University of China – sequence: 6 givenname: Jiaxin surname: Li fullname: Li, Jiaxin organization: Faculty of Information Science and Engineering, Ocean University of China – sequence: 7 givenname: Wendong surname: Li fullname: Li, Wendong organization: Faculty of Information Science and Engineering, Ocean University of China – sequence: 8 givenname: Zhiqiang surname: Wei fullname: Wei, Zhiqiang organization: Faculty of Information Science and Engineering, Ocean University of China, High Performance Computing Center, Pilot National Laboratory for Marine Science and Technology (Qingdao) – sequence: 9 givenname: Yongjian surname: Gu fullname: Gu, Yongjian email: yjgu@ouc.edu.cn organization: Faculty of Information Science and Engineering, Ocean University of China |
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| Cites_doi | 10.1088/2058-9565/abae7d 10.1088/1367-2630/15/1/013021 10.1103/PhysRevA.99.022341 10.1103/RevModPhys.91.035001 10.1137/16M1087072 10.22331/q-2018-08-06-79 10.1007/s00220-020-03699-z 10.1103/PhysRevLett.118.010501 10.1016/j.compfluid.2012.01.014 10.1038/s41598-020-79777-y 10.1103/PhysRevA.101.022308 10.1038/s41586-019-1666-5 10.1063/1.5089550 10.1103/PhysRevA.100.032306 10.1007/s00220-017-3002-y 10.22331/q-2021-11-10-574 10.1103/PhysRevA.99.012323 10.1103/PhysRevA.69.032315 10.1103/PhysRevLett.103.150502 10.1103/PhysRevA.76.052310 10.1103/PhysRevA.52.3457 10.1007/s11128-020-02669-7 10.1016/j.compfluid.2018.03.080 10.4169/amer.math.monthly.121.02.120 10.1038/s41586-019-1427-5 10.1137/1.9781611971446 10.1088/1751-8113/47/10/105301 10.1109/SFCS.2000.892140 10.1038/s41598-020-75730-1 10.26421/QIC12.3-4-6 10.1145/3287624.3287704 10.1007/s11128-020-02855-7 10.26421/QIC16.3-4-2 10.1109/ISPA.2001.938674 10.1109/FOCS.2015.54 10.1038/npjqi.2015.23 10.1109/SFCS.1994.365700 |
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| Keywords | Matrix diagonalization Quantum linear systems algorithm Poisson equation Quantum arithmetic |
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