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arXiv:2505.10842 · IEEE Access

Accelerating Parameter Initialization in Quantum Chemical Simulations via LSTM-FC-VQE

Ran-Yu Chang, Yu‐Cheng Lin, Pei-Che Hsu, Tsung‐Wei Huang, En-Jui Kuo

Published Jan 1, 2025• 3 citations
arXivHTMLPDF

Abstract

Variational Quantum Eigensolver (VQE) is a leading algorithm for quantum chemistry on near-term devices, but its performance is often limited by inefficient parameter initialization, which leads to slow convergence and high computational overhead. While meta-learning approaches such as LSTM-VQE have been proposed to predict optimization trajectories, their applicability remains restricted by rigid ansatz structures and molecule-specific parameter dimensions. To address these limitations, we propose LSTM-FC-VQE, an enhanced meta-learning framework that combines Long Short-Term Memory (LSTM) networks with a fully connected projection layer. This design enables the model to standardize variable-length parameter inputs, allowing it to handle molecular systems with heterogeneous qubit counts and ansatz architectures more effectively. We validate our approach on benchmark molecules, including H4and H2O, and demonstrate that LSTM-FC-VQE significantly reduces the number of VQE iterations required for convergence while achieving energy accuracies comparable to full configuration interaction (FCI) results. Beyond accelerating convergence, our method generalizes to unseen molecular configurations with minimal training data, offering a scalable and data-efficient strategy for quantum chemical simulations in the NISQ era.

DOI
10.1109/access.2025.3628966

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Variational Quantum Eigensolver (VQE) is a leading algorithm for quantum chemistry on near-term devices, but its performance is often limited by inefficient parameter initialization, which leads to slow convergence and high computational overhead. While meta-learning approaches such as LSTM-VQE have been proposed to predict optimization trajectories, their applicability remains restricted by rigid ansatz structures and molecule-specific parameter dimensions. To address these limitations, we propose LSTM-FC-VQE, an enhanced meta-learning framework that combines Long Short-Term Memory (LSTM) networks with a fully connected projection layer. This design enables the model to standardize variable-length parameter inputs, allowing it to handle molecular systems with heterogeneous qubit counts and ansatz architectures more effectively. We validate our approach on benchmark molecules, including H4and H2O, and demonstrate that LSTM-FC-VQE significantly reduces the number of VQE iterations required for convergence while achieving energy accuracies comparable to full configuration interaction (FCI) results. Beyond accelerating convergence, our method generalizes to unseen molecular configurations with minimal training data, offering a scalable and data-efficient strategy for quantum chemical simulations in the NISQ era.
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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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