We present a novel quantum generative framework based on Quantum Long Short-Term Memory (QLSTM) networks to optimize the sampling of Slater determinants in Full Configuration Interaction (FCI), a key method in quantum chemistry for solving the Schrödinger equation. Our model employs variational quantum circuits to learn an approximate distribution over the configuration space, guiding the generation of new, physically meaningful determinants. This distribution reflects the correlations among significant electronic configurations, allowing for a guided exploration of the determinant space and accelerating convergence toward reference energies. By framing determinant selection as a generative modeling task, our approach contributes to the emerging field of quantum generative AI applied to many-body systems. Implemented using Pennylane and accelerated with JAX, the QLSTM model converges faster than both classical LSTM and random baselines. Notably, it exhibits stable and consistent convergence across different hyperparameter settings, suggesting that the model captures an underlying physical structure rather than overfitting to specific training conditions. Our results demonstrate the scalability and physical consistency of hybrid quantum-classical generative models for quantum chemistry tasks.
We present a novel quantum generative framework based on Quantum Long Short-Term Memory (QLSTM) networks to optimize the sampling of Slater determinants in Full Configuration Interaction (FCI), a key method in quantum chemistry for solving the Schrödinger equation. Our model employs variational quantum circuits to learn an approximate distribution over the configuration space, guiding the generation of new, physically meaningful determinants. This distribution reflects the correlations among significant electronic configurations, allowing for a guided exploration of the determinant space and accelerating convergence toward reference energies. By framing determinant selection as a generative modeling task, our approach contributes to the emerging field of quantum generative AI applied to many-body systems. Implemented using Pennylane and accelerated with JAX, the QLSTM model converges faster than both classical LSTM and random baselines. Notably, it exhibits stable and consistent convergence across different hyperparameter settings, suggesting that the model captures an underlying physical structure rather than overfitting to specific training conditions. Our results demonstrate the scalability and physical consistency of hybrid quantum-classical generative models for quantum chemistry tasks.
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.
Abstract We propose a data-driven approach using a restricted Boltzmann machine (RBM) to solve the Schrödinger equation in configuration space. Traditional configuration interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble radial distribution functions linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry
Directly solving the full electron-nuclear Schrödinger equation remains one of the grand challenges in quantum mechanics. Here, we propose a quantum-chemically motivated orbital-based neural network wavefunction ansatz with explicit many-body electron-electron correlation terms, with parameters depending on the entire electron-nuclear configuration, enabling an accurate description of strongly correlated and/or multi-reference electronic structures by a single Slater-determinant across a broad nuclear configuration space. To train this wavefunction, we further develop an efficient hybrid optimization strategy that combines the variational Monte Carlo technique with local-energy constraints, mitigating the intrinsic sampling bias of the former and considerably reducing the statistical error. These advances are embedded in a unified neural network framework, Schrödinger, enabling the determination of globally accurate potential energy surfaces with a single training for systems ranging from strongly correlated diatomic molecules, triatomic reactions containing conical intersections, to polyatomic multi-reference molecules. This work offers a practical machine-learning tool for solving the electron-nuclear Schrödinger equation and capturing full quantum effects beyond the Born-Oppenheimer approximation.
Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic ``Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of ``quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling such as natural language processing, speech recognition on noisy intermediate-scale quantum (NISQ) devices.