用量子序列模型自动优化量子算法初始参数,提速且效果更好。
Meta-Learning for Quantum Optimization via Quantum Sequence Model
- 用量子核LSTM学习生成优化参数的策略
- 在10~13个节点的图上逼近比最高,收敛最快
- 仅43个参数就实现跨规模快速迁移,适合量子硬件
量子近似优化算法(QAOA)是解决组合优化问题的主流方法,但变分参数的选取因能量景观非凸而困难,常导致收敛慢、解质量差。本文提出一种量子元学习框架,训练先进量子序列模型生成有效的参数初始化策略。研究了四种经典或量子序列模型,包括基于量子核的长短期记忆网络(QK-LSTM),在“学会学习”范式下作为可学习优化器。数值实验表明,QK-LSTM在最大割问题(Max-Cut)上表现最优,对所有测试规模(n=10至13)均获得最高逼近比和最快收敛速度。关键优势在于其能合成单一固定的最佳参数集,实现完美参数可迁移性,即使推广到更大规模问题仍保持显著加速。该能力得益于量子核架构的紧凑性和表达力。仅含43个可训练参数的QK-LSTM,显著优于含56个参数的经典LSTM及其他量子序列模型,为当前量子计算时代变分量子算法的高效参数初始化提供了可靠路径。
原文摘要 · Abstract (English)
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for solving combinatorial optimization problems on near-term quantum processors. However, finding good variational parameters remains a significant challenge due to the non-convex energy landscape, often resulting in slow convergence and poor solution quality. In this work, we propose a quantum meta-learning framework that trains advanced quantum sequence models to generate effective parameter initialization policies. We investigate four classical or quantum sequence models, including the Quantum Kernel-based Long Short-Term Memory (QK-LSTM), as learned optimizers in a "learning to learn" paradigm. Our numerical experiments on the Max-Cut problem demonstrate that the QK-LSTM optimizer achieves superior performance, obtaining the highest approximation ratios and exhibiting the fastest convergence rate across all tested problem sizes (n=10 to 13). Crucially, the QK-LSTM model achieves perfect parameter transferability by synthesizing a single, fixed set of near-optimal parameters, leading to a remarkable sustained acceleration of convergence even when generalizing to larger problems. This capability, enabled by the compact and expressive power of the quantum kernel architecture, underscores its effectiveness. The QK-LSTM, with only 43 trainable parameters, substantially outperforms the classical LSTM (56 parameters) and other quantum sequence models, establishing a robust pathway toward highly efficient parameter initialization for variational quantum algorithms in the NISQ era.
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