Meta-Learning for Quantum Optimization via Quantum Sequence Model
This work addresses a critical bottleneck in variational quantum algorithms for combinatorial optimization, offering a robust pathway toward efficient parameter initialization in the NISQ era.
The paper tackles the challenge of finding good variational parameters for the Quantum Approximate Optimization Algorithm (QAOA) by proposing a quantum meta-learning framework that trains quantum sequence models to generate effective parameter initialization policies, with the QK-LSTM optimizer achieving the highest approximation ratios and fastest convergence rates on Max-Cut problems (n=10 to 13) using only 43 trainable parameters.
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.