Using Variational Quantum Algorithm to Solve the LWE Problem
The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy int...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/10/1428 |
| _version_ | 1827650288086941696 |
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| author | Lihui Lv Bao Yan Hong Wang Zhi Ma Yangyang Fei Xiangdong Meng Qianheng Duan |
| author_facet | Lihui Lv Bao Yan Hong Wang Zhi Ma Yangyang Fei Xiangdong Meng Qianheng Duan |
| author_sort | Lihui Lv |
| collection | DOAJ |
| description | The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions. |
| first_indexed | 2024-03-09T20:14:13Z |
| format | Article |
| id | doaj.art-0fe8589148d34a0482ced605da9fe2ba |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:14:13Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0fe8589148d34a0482ced605da9fe2ba2023-11-24T00:03:36ZengMDPI AGEntropy1099-43002022-10-012410142810.3390/e24101428Using Variational Quantum Algorithm to Solve the LWE ProblemLihui Lv0Bao Yan1Hong Wang2Zhi Ma3Yangyang Fei4Xiangdong Meng5Qianheng Duan6State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, ChinaThe variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions.https://www.mdpi.com/1099-4300/24/10/1428quantumLWEQAOAVQEKYBER |
| spellingShingle | Lihui Lv Bao Yan Hong Wang Zhi Ma Yangyang Fei Xiangdong Meng Qianheng Duan Using Variational Quantum Algorithm to Solve the LWE Problem Entropy quantum LWE QAOA VQE KYBER |
| title | Using Variational Quantum Algorithm to Solve the LWE Problem |
| title_full | Using Variational Quantum Algorithm to Solve the LWE Problem |
| title_fullStr | Using Variational Quantum Algorithm to Solve the LWE Problem |
| title_full_unstemmed | Using Variational Quantum Algorithm to Solve the LWE Problem |
| title_short | Using Variational Quantum Algorithm to Solve the LWE Problem |
| title_sort | using variational quantum algorithm to solve the lwe problem |
| topic | quantum LWE QAOA VQE KYBER |
| url | https://www.mdpi.com/1099-4300/24/10/1428 |
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