Meta-Learning for Quantum Optimization via Quantum Sequence Model

TL;DR

This paper introduces a quantum meta-learning framework using quantum sequence models, notably QK-LSTM, to improve parameter initialization in QAOA, leading to faster convergence and better solutions for combinatorial optimization.

Contribution

It develops a quantum meta-learning approach with quantum sequence models, especially QK-LSTM, for effective parameter initialization in QAOA, demonstrating superior performance and transferability.

Findings

QK-LSTM achieves highest approximation ratios.

QK-LSTM exhibits fastest convergence across problem sizes.

Single fixed parameters enable transferability to larger problems.

Abstract

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.