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Using small-scale quantum devices to solve algebraic equations

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Abstract

Solving algebraic equations over GF(2) is a problem which has a wide range of applications, including NP-Hard problems and problems related to cryptography. The existing mature algorithms are difficult to solve large-scale problems. Inspired by Schöning’s algorithm and its quantum version, we apply related methods to solve algebraic equations over GF (2). The new algorithm we proposed has a significant improvement of solving efficiency in large-scale and sparse algebraic equations. As a hybrid algorithm, the new algorithm can not only run on a classic computer alone, but also use small-scale quantum devices to assist acceleration. And the new algorithm can be seen as an example of solving a large-scale problem on a small-scale quantum device.

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Authors and Affiliations

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450001, China

    Hongshu Li, Zhi Ma, Hong Wang, Qianheng Duan, Yangyang Fei & Xiangdong Meng

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  1. Hongshu Li
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  2. Zhi Ma
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  3. Hong Wang
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  4. Qianheng Duan
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  5. Yangyang Fei
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  6. Xiangdong Meng
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Correspondence to Hong Wang.

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This work was supported in part by the National Natural Science Foundation of China (Grants Nos. 61972413, 61701539, 61901525), and in part by the National Cryptography Development Fund (mmjj20180107, mmjj20180212).

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Li, H., Ma, Z., Wang, H. et al. Using small-scale quantum devices to solve algebraic equations. Quantum Inf Process 20, 140 (2021). https://doi.org/10.1007/s11128-021-03064-6

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