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Meta-Learning for Quantum Optimization via Quantum Sequence Model

Yu-Cheng Lin, Yu-Chao Hsu, Samuel Yen-Chi Chen

TL;DR

The paper tackles the challenge of initializing QAOA parameters for Max-Cut on near-term quantum devices by casting parameter selection as a meta-learning problem. It introduces four quantum sequence models (QK-LSTM, QLSTM, LSTM, QFWP) to predict initialization policies, with QK-LSTM delivering the best performance: rapid convergence, superior approximation ratios, and transferability to larger instances using a compact 43-parameter model. The two-phase testing protocol—recurrent initialization followed by classical fine-tuning—demonstrates substantial reductions in quantum-classical optimization iterations compared to standard QAOA. This work presents a promising pathway for efficient, scalable variational quantum algorithm deployment in the NISQ era and suggests extensions to broader quantum optimization tasks.

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.

Meta-Learning for Quantum Optimization via Quantum Sequence Model

TL;DR

The paper tackles the challenge of initializing QAOA parameters for Max-Cut on near-term quantum devices by casting parameter selection as a meta-learning problem. It introduces four quantum sequence models (QK-LSTM, QLSTM, LSTM, QFWP) to predict initialization policies, with QK-LSTM delivering the best performance: rapid convergence, superior approximation ratios, and transferability to larger instances using a compact 43-parameter model. The two-phase testing protocol—recurrent initialization followed by classical fine-tuning—demonstrates substantial reductions in quantum-classical optimization iterations compared to standard QAOA. This work presents a promising pathway for efficient, scalable variational quantum algorithm deployment in the NISQ era and suggests extensions to broader quantum optimization tasks.

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.

Paper Structure

This paper contains 15 sections, 13 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Quantum Sequence Model
  3. Classical Long Short-Term Memory
  4. Quantum Long Short-Term Memory
  5. Quantum Kernel-Based Long Short-Term Memory
  6. Quantum FWP
  7. Method
  8. Quantum Approximate Optimization Algorithms for MaxCut
  9. Meta-Learning Framework for QAOA
  10. Optimization Protocol
  11. Model Training (Meta-Learning)
  12. Test Optimization Protocol
  13. Results
  14. Discussion
  15. Conclusion and Future Work

Figures (9)

  • Figure 1: Schematic representation of the LSTM.
  • Figure 2: Schematic representation of the VQC.
  • Figure 3: Schematic representation of the QLSTM.
  • Figure 4: Schematic illustration of the QK-LSTM and the quantum circuit representation of $U(x_i, w)$ and $U^{\dagger}(x_j, w)$, demonstrating the use of quantum gates for encoding data and extracting features for machine learning applications.
  • Figure 5: Schematic representation of the QFWP.
  • ...and 4 more figures