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Physica A Statistical Mechanics and its Applications

Near-term quantum algorithm for solving the MaxCut problem with fewer quantum resources

Zhao Xiumei, Yongmei Li, Jing Li, Shasha Wang, Song Wang, Su‐Juan Qin, Fei Gao

Published Jul 17, 2024• 8 citations
Publisher
DOI
10.1016/j.physa.2024.129951

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The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a challenge related to the optimization of its free parameters, which requires the usage of resourceintensive evolutionary or even global optimization algorithms. We propose a newlog⁡Q\log QlogQparameterization that can be optimized with a gradient-inspired method, which is less resource-intensive and thus strengthens the advantage of LogQ over QAOA for large/industrial problems. We illustrate the features of our method on an analytical model and present larger scale numerical results on MaxCut problems.
A quantum approximate optimization algorithm (QAOA) is a polynomial-time approximate optimization algorithm used to solve combinatorial optimization problems. However, the existing QAOA algorithms have poor generalization performance in finding an optimal solution from a feasible solution set of combinatorial problems. In order to solve this problem, a quantum approximate optimization algorithm with metalearning for the MaxCut problem (MetaQAOA) is proposed. Specifically, a quantum neural network (QNN) is constructed in the form of the parameterized quantum circuit to detect different topological phases of matter, and a classical long short-term memory (LSTM) neural network is used as a black-box optimizer, which can quickly assist QNN to find the approximate optimal QAOA parameters. The experiment simulation via TensorFlow Quantum (TFQ) shows that MetaQAOA requires fewer iterations to reach the threshold of the loss function, and the threshold of the loss value after training is smaller than comparison methods. In addition, our algorithm can learn parameter update heuristics which can generalize to larger system sizes and still outperform other initialization strategies of this scale.
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually outperform classical schemes, they suffer from resource constraints and trainability issues such as barren plateaus, making large-scale instances intractable on noisy intermediate-scale quantum devices. In this paper, we propose an enhanced distributed variational quantum eigensolver for large-scale MaxCut problems, which extends our prior distributed variational quantum eigensolver framework by integrating a novel hybrid classical-quantum perturbation strategy, enhances optimization scalability and efficiency. Our algorithm solves weighted MaxCut instances with up to 1000 vertices using only 10 qubits, and numerical results indicate that it consistently outperforms the Goemans-Williamson algorithm. We further employ a warm-start initialization strategy, seeding the algorithm with high-quality solutions from the Goemans-Williamson algorithm, with results confirming that the optimal classical solution can be effectively further improved. The practical utility of the proposed algorithm is further validated through its application to haplotype phasing on genome sequencing data of the human ABCA1 gene, producing high-quality haplotypes that rival those obtained by the Goemans-Williamson algorithm with 10610^6106 projections. These results establish the proposed algorithm as a scalable, NISQ-compatible framework for near-term quantum-enhanced large-scale combinatorial optimization.