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International Conference on Advanced Computational Intelligence (ICACI)

A General RNN Model for Reconstructing Arbitrary Wave Functions

Shuang Cong, Li‐Min Lin

Published Jul 7, 2025• 1 citation
Publisher

Abstract

A general recurrent neural network (RNN) model is proposed for reconstructing wave functions with varying parameters. This model is suitable for both real and complex ground-state wave functions in condensed matter physics models. We propose three straightforward techniques for integrating variable parameters, enabling the reconstruction of an entire quantum state family within a unified RNN model through numerical augmentation and concatenation. This innovation significantly broadens the model's generalization capabilities. The core unit for wave function reconstruction in the RNN is the gated recurrent unit (GRU), and the RNN's autoregressive property is utilized to generate independent training samples. The training of the network employs a variational Monte Carlo (VMC) optimization strategy. The proposed RNN is applied to two classical condensed matter physics models: the one-dimensional (1D) transverse field Ising model (TFIM) and the 1D J1-J2 model, and it successfully reconstructs arbitrary wave functions. In numerical experiments conducted on a 4-qubit system, using exact diagonalization (ED) as a reference method and relative energy error as a performance indicator, our real- and complex-valued general RNNs demonstrate remarkable reconstruction and generalization performance of wave functions under different physical parameters. To further refine accuracy and reduce training time, we fine-tune the designed network using target samples from a few specific tasks. We present an efficient and accurate general generation model for reconstructing arbitrary wave functions to better accommodate the diversity and variability encountered in practical applications.

DOI
10.1109/icaci65340.2025.11096259

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•May 22, 2019•0 citations
A general recurrent neural network (RNN) model is proposed for reconstructing wave functions with varying parameters. This model is suitable for both real and complex ground-state wave functions in condensed matter physics models. We propose three straightforward techniques for integrating variable parameters, enabling the reconstruction of an entire quantum state family within a unified RNN model through numerical augmentation and concatenation. This innovation significantly broadens the model's generalization capabilities. The core unit for wave function reconstruction in the RNN is the gated recurrent unit (GRU), and the RNN's autoregressive property is utilized to generate independent training samples. The training of the network employs a variational Monte Carlo (VMC) optimization strategy. The proposed RNN is applied to two classical condensed matter physics models: the one-dimensional (1D) transverse field Ising model (TFIM) and the 1D J1-J2 model, and it successfully reconstructs arbitrary wave functions. In numerical experiments conducted on a 4-qubit system, using exact diagonalization (ED) as a reference method and relative energy error as a performance indicator, our real- and complex-valued general RNNs demonstrate remarkable reconstruction and generalization performance of wave functions under different physical parameters. To further refine accuracy and reduce training time, we fine-tune the designed network using target samples from a few specific tasks. We present an efficient and accurate general generation model for reconstructing arbitrary wave functions to better accommodate the diversity and variability encountered in practical applications.
Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical observables. In this paper, we employ a recurrent neural network (RNN) to reconstruct the ground state of the spin-1/2 XYXYXY model, a prototypical Hamiltonian explored in trapped ion simulators. We explore its performance after enforcing a U(1) symmetry, which was recently shown by Hibat-Allah et al. [Phys. Rev. Res. 2, 023358 (2020)] to preserve the autoregressive nature of the RNN. By studying the reconstruction of the XYXYXY model ground state from projective measurement data, we show that imposing U(1) symmetry on the RNN significantly increases the efficiency of learning, particularly in the early epoch regime. We argue that this performance increase may result from the tendency of the enforced symmetry to alleviate vanishing and exploding gradients, which helps stabilize the training process. Thus, symmetry-enforced RNNs may be particularly useful for applications of quantum simulators where a rapid feedback between optimization and circuit preparation is necessary, such as in hybrid classical-quantum algorithms.
Abstract Neural-network quantum states (NQS) are powerful neural-network ansätzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be systematically improvable by increasing the number of parameters. Here we demonstrate an Adaptive scheme to optimize NQSs, through the example of recurrent neural networks (RNNs), using a fraction of the computation cost while reducing training fluctuations and improving the quality of variational calculations targeting ground states of prototypical models in one- and two-spatial dimensions. This Adaptive framework reduces the computational cost through training small RNNs and reusing them to initialize larger RNNs. This work opens up the possibility for optimizing graphical processing unit resources deployed in large-scale NQS simulations.
Non-Hermitian (NH) quantum systems have emerged as a powerful framework for describing open quantum systems, nonequilibrium dynamics, and engineered quantum optical materials. However, solving the ground-state properties of NH systems is challenging due to the exponential scaling of the Hilbert space and exotic phenomena such as the emergence of exceptional points. Another challenge arises from the limitations of traditional methods like exact diagonalization (ED). For the past decade, neural networks (NNs) have shown promise in approximating many-body wavefunctions, yet their application to NH systems remains largely unexplored. In this paper, we explore different NN architectures to investigate the ground-state properties of a parity-time-symmetric, one-dimensional NH, transverse field Ising model with a complex spectrum by employing a recurrent neural network (RNN), a restricted Boltzmann machine (RBM), and a multilayer perceptron (MLP). We construct the NN-based many-body wavefunctions and validate our approach by recovering the ground-state properties of the model for small system sizes, finding excellent agreement with ED. Furthermore, for larger system sizes, we demonstrate that the RNN outperforms both the RBM and MLP. However, we show that the accuracy of the RBM and MLP can be significantly improved through transfer learning, allowing them to perform comparably to the RNN for larger system sizes. These results highlight the potential of neural-network-based approaches—particularly for accurately capturing the low-energy physics of NH quantum systems in case of both weak and strong non-Hermiticity.
Abstract Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness recurrent neural networks (RNNs). However, while their predictions are quite accurate, their learning process is complex and, thus, time and energy consuming. Here, we propose to extend the concept of RRNs by including continuous-variable quantum resources in it and to use a quantum-enhanced RNN to overcome these obstacles. The design of the continuous-variable quantum RNN (CV-QRNN) is rooted in the continuous-variable quantum computing paradigm. By performing extensive numerical simulations, we demonstrate that the quantum network is capable of learning-time dependence of several types of temporal data and that it converges to the optimal weights in fewer epochs than a classical network. Furthermore, for a small number of trainable parameters, it can achieve lower losses than its classical counterpart. CV-QRNN can be implemented using commercially available quantum-photonic hardware.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Machine learning (ML) architectures such as convolutional neural networks (CNNs) have garnered considerable recent attention in the study of quantum many-body systems. However, advanced ML approaches such as gated recurrent neural networks (RNNs) have seldom been applied to such contexts. Here we demonstrate that a special class of RNNs known as long short-term memory (LSTM) networks is capable of learning and accurately predicting the time evolution of one-dimensional (1D) Ising model with simultaneous transverse and parallel magnetic fields, as quantitatively corroborated by relative entropy measurements and magnetization between the predicted and exact state distributions. In this unsupervised learning task, the many-body state evolution was predicted in an autoregressive way from an initial state, without any guidance or knowledge of any Hamiltonian. Our work paves the way for future applications of advanced ML methods in quantum many-body dynamics without relying on the explicit form of the Hamiltonian.