Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929206338781184 |
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| author | Wang, Sha-Sha Liu, Hai-Ling Li, Yong-Mei Gao, Fei Qin, Su-Juan Wen, Qiao-Yan |
| author_facet | Wang, Sha-Sha Liu, Hai-Ling Li, Yong-Mei Gao, Fei Qin, Su-Juan Wen, Qiao-Yan |
| contents | The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For constrained optimization problems with unconstrained variables, which we call Unconstrained-Variables Problems (UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single-qubit rotating gates $R_X$ operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two-qubit gates and the parameter sharing in the $R_X$, which consequently impacts the performance of QAOA+ for solving UVPs. Therefore, it is crucial to develop a suitable ansatz for UVPs. In this paper, we propose the Variational Quantum Algorithm-Preserving Feasible Space (VQA-PFS) ansatz, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware-Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA-PFS significantly enhances the success probability and exhibits faster convergence compared to QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA-PFS reduces the circuit depth dramatically in comparison to QAOA+ and QAOA. Our algorithm is general and instructive in tackling UVPs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06922 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem Wang, Sha-Sha Liu, Hai-Ling Li, Yong-Mei Gao, Fei Qin, Su-Juan Wen, Qiao-Yan Quantum Physics The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For constrained optimization problems with unconstrained variables, which we call Unconstrained-Variables Problems (UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single-qubit rotating gates $R_X$ operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two-qubit gates and the parameter sharing in the $R_X$, which consequently impacts the performance of QAOA+ for solving UVPs. Therefore, it is crucial to develop a suitable ansatz for UVPs. In this paper, we propose the Variational Quantum Algorithm-Preserving Feasible Space (VQA-PFS) ansatz, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware-Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA-PFS significantly enhances the success probability and exhibits faster convergence compared to QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA-PFS reduces the circuit depth dramatically in comparison to QAOA+ and QAOA. Our algorithm is general and instructive in tackling UVPs. |
| title | Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.06922 |