A Review of Algorithms and Applications of Solvers with Quantum Computing Acceleration

doi:10.19596/j.cnki.1001-246x.8778

Abstract

Abstract:

Quantum computing is a new computing model based on the principles of quantum mechanics. Because of its powerful parallelism far superior to classical computing, quantum computing is considered as a computational method that may have a subversive impact on the future, providing a new way to solve some complex problems. The algorithms and applications of quantum solvers in numerical computation-related problems of large-scale science and engineering are reviewed. In particular, systems of linear equations, eigenvalue problems, differential equations, Hamiltonian and graph computation, quantum machine learning, quantum solver platform, and practical numerical simulation have been introduced. Aiming at different numerical computing problems, the current mainstream quantum computing algorithms are introduced in detail, and the research progress of relevant algorithms at home and abroad in recent years is comprehensively summarized. Finally, the future development trend of quantum computing in numerical algebra solving is prospected.

Key words: quantum computing, quantum solver, quantum parallelism, equation solving

CLC Number:

TP3-0

Kang XU, Zeyang LI, Zhufeng GUO, Yingtong SHEN, Wei WANG, Minhui GOU, Zizheng WANG, Yukun WANG, Weifeng LIU. A Review of Algorithms and Applications of Solvers with Quantum Computing Acceleration[J]. Chinese Journal of Computational Physics, 2024, 41(1): 131-150.

Figures/Tables 3

Fig.1 Overall circuit diagram of HHL algorithm

Fig.2 Schematic diagram of the Variational Quantum Algorithm (The classical optimizer is used to train theparameterized quantum circuits, in which quantum computer uses the parameterized unitary gates to process thecomputationally difficult subroutines of the whole algorithm and the classical computer is responsible for theiterative updating of parameters, such as gradient descent algorithm.)

Table 1 The language and performance parameters used by some quantum cloud platforms

量子云平台	语言	性能
百度量易伏	Python, C++	8个量子比特T1^①: 31.0 μs T2^②: 8.7 μs保真度^③：99.80%
华为HiQ	Python	11个量子比特
本源	Python, C++	12个量子比特T1: 20.82 μs T2: 4.14 μs保真度：99.78%
IBM	Python	433个量子比特T1: 91.12 μs T2: 59.94 μs保真度：99.47%

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