Abstract A high-dimensional generalized wave function probability distribution reconstruction model is proposed in this paper to investigate the generalization performance of the ground-state wave functions in the reconstructed high-qubit transverse-field Ising model. By leveraging the autoregressive properties of Mamba and combining them with an efficient sampling process, independent training samples can be automatically generated without the need for additional labeled samples. By combining multi-ground-state scaling with the variational Monte Carlo optimization strategy, the model trains the weights of the high-qubit universal wave function using only a small number of different physical parameters within a limited range. In numerical simulation experiments of wave function reconstruction for a 40-qubit system, the model weights are trained using only partial values of external field strength ranging from 0.5 to 1.5, and the model achieves high-precision universal wave function reconstruction of quantum state families with external field strengths ranging from 0 to 2. In numerical simulation experiments of wave function reconstruction for systems with qubits ranging from 40 to 80, the proposed model exhibits better generalization ability and more efficient inference performance, providing an efficient and accurate generalized reconstruction method for the ground-state probability distribution of high-qubit systems.
Fund:National Natural Science Foundation of China(No.62473354)
Corresponding Authors:
CONG Shuang, Ph.D., professor. Her research interests include advanced control strategies, artificial neural networks, intelligent control and quantum system control.
About author:: LIN Limin, Master student. Her research interests include quantum state reconstruction and deep learning.
[1] FOULKES W M C, MITAS L, NEEDS R J, et al. Quantum Monte Carlo Simulations of Solids. Reviews of Modern Physics, 2001, 73(1): 33-83. [2] SCHOLLWÖCK U. The Density-Matrix Renormalization Group in the Age of Matrix Product States. Annals of Physics, 2011, 326(1): 96-192. [3] DE OLIVEIRA N M, PARK D K, ARAUJO I F, et al. Quantum Variational Distance-Based Centroid Classifier. Neurocomputing, 2024, 576. DOI: 10.1016/j.neucom.2024.127356. [4] SAITO H. Solving the Bose-Hubbard Model with Machine Learning. Journal of the Physical Society of Japan, 2017, 86(9). DOI: 10.7566/JPSJ.86.093001. [5] SAITO H, KATO M. Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice. Journal of the Physical Society of Japan, 2018, 87(1). DOI: 10.7566/JPSJ.87.014001. [6] LIANG X, LIU W Y, LIN P Z, et al. Solving Frustrated Quantum Many-Particle Models with Convolutional Neural Networks. Physical Review B, 2018, 98(10). DOI: 10.1103/PhysRevB.98.104426. [7] PFEUTY P. The One-Dimensional Ising Model with a Transverse Field. Annals of Physics, 1970, 57(1): 79-90. [8] CARLEO G, TROYER M. Solving the Quantum Many-Body Pro-blem with Artificial Neural Networks. Science, 2017, 355(6325): 602-606. [9] CARLEO G, NOMURA Y, IMADA M. Constructing Exact Representations of Quantum Many-Body Systems with Deep Neural Networks. Nature Communications, 2018, 9(1). DOI: 10.1038/s41467-018-07520-3. [10] HIBAT-ALLAH M, GANAHL M, HAYWARD L E, et al. Recu-rrent Neural Network Wave Functions. Physical Review Research, 2020, 2(2). DOI: 10.1103/physrevresearch.2.023358. [11] ZHANG Y H, DI VENTRA M. Transformer Quantum State: A Multipurpose Model for Quantum Many-Body Problems. Physical Review B, 2023, 107(7). DOI: 10.1103/PhysRevB.107.075147. [12] BROOKS S, GELMAN A, JONES G, et al. Handbook of Markov Chain Monte Carlo. New York, USA: CRC Press, 2011. [13] BARRETT T D, MALYSHEV A, LVOVSKY A I. Autoregressive Neural-Network Wavefunctions for ab initio Quantum Chemistry. Nature Machine Intelligence, 2022, 4(4): 351-358. [14] VASWANI A, SHAZEER N, PARMAR N, et al. Attention Is All You Need // Proc of the 31st International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2017: 6000-6010. [15] DOSOVITSKIY A, BEYER L, KULESNIKOV A, et al. An Image Is Worth 16×16 Words: Transformers for Image Recognition at Scale[C/OL]. [2024-11-06]. https://arxiv.org/pdf/2010.11929. [16] LIU Z, LIN Y T, CAO Y, et al. Swin Transformer: Hierarchical Vision Transformer Using Shifted Windows // Proc of the IEEE/CVF International Conference on Computer Vision. Washington, USA: IEEE, 2021: 9992-10002. [17] DONG L H, XU S, XU B. Speech-Transformer: A No-recurrence Sequence-to-Sequence Model for Speech Recognition // Proc of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington, USA: IEEE, 2018: 5884-5888. [18] VELICˇKOVIC＇ P, CUCURULL G, CASANOVA A, et al. Graph Attention Networks[C/OL]. [2024-11-06]. https://arxiv.org/pdf/1710.10903. [19] GU A, DAO T. Mamba: Linear-Time Sequence Modeling with Selective State Spaces[C/OL]. [2024-11-06]. https://arxiv.org/pdf/2312.00752. [20] KINGMA D P, BA J L. Adam: A Method for Stochastic Optimization[C/OL]. [2024-11-06]. https://arxiv.org/pdf/1412.6980. [21] BROWN T B, MANN B, RYDER N, et al. Language Models Are Few-Shot Learners // Proc of the 34th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2020: 1877-1901.
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