Hybrid GRU-CNN Bilinear Parameters Initialization for Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2311.07869v1
• Date: Tue, 14 Nov 2023 03:00:39 GMT
• Title: Hybrid GRU-CNN Bilinear Parameters Initialization for Quantum Approximate Optimization Algorithm
• Authors: Zuyu Xu, Pengnian Cai, Kang Sheng, Tao Yang, Yuanming Hu, Yunlai Zhu, Zuheng Wu, Yuehua Dai, Fei Yang
• Abstract summary: We propose a hybrid optimization approach that integrates Gated Recurrent Units (GRU), Conal Neural Networks (CNN), and a bilinear strategy as an innovative alternative to conventional approximations for predicting optimal parameters of QAOA circuits. We employ the bilinear strategy to initialize to QAOA circuit parameters at greater depths, with reference parameters obtained from GRU-CNN optimization.
• Score: 7.502733639318316
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Approximate Optimization Algorithm (QAOA), a pivotal paradigm in the realm of variational quantum algorithms (VQAs), offers promising computational advantages for tackling combinatorial optimization problems. Well-defined initial circuit parameters, responsible for preparing a parameterized quantum state encoding the solution, play a key role in optimizing QAOA. However, classical optimization techniques encounter challenges in discerning optimal parameters that align with the optimal solution. In this work, we propose a hybrid optimization approach that integrates Gated Recurrent Units (GRU), Convolutional Neural Networks (CNN), and a bilinear strategy as an innovative alternative to conventional optimizers for predicting optimal parameters of QAOA circuits. GRU serves to stochastically initialize favorable parameters for depth-1 circuits, while CNN predicts initial parameters for depth-2 circuits based on the optimized parameters of depth-1 circuits. To assess the efficacy of our approach, we conducted a comparative analysis with traditional initialization methods using QAOA on Erd\H{o}s-R\'enyi graph instances, revealing superior optimal approximation ratios. We employ the bilinear strategy to initialize QAOA circuit parameters at greater depths, with reference parameters obtained from GRU-CNN optimization. This approach allows us to forecast parameters for a depth-12 QAOA circuit, yielding a remarkable approximation ratio of 0.998 across 10 qubits, which surpasses that of the random initialization strategy and the PPN2 method at a depth of 10. The proposed hybrid GRU-CNN bilinear optimization method significantly improves the effectiveness and accuracy of parameters initialization, offering a promising iterative framework for QAOA that elevates its performance.

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