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arXiv · 2312.06922

Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem

Sha-Sha Wang·Hai-Ling Liu·Yong-Mei Li·Fei Gao·Su-Juan Qin·Qiao-Yan Wen
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Abstract

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.

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Sha-Sha Wang, Hai-Ling Liu, Yong-Mei Li, Fei Gao, Su-Juan Qin, Qiao-Yan Wen. 2023-12-12. Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem. https://arxiv.org/abs/2312.06922

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