Machine learning identification of symmetrized base states of Rydberg atoms

Abstract

Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.

Graphical abstract

Keywords

Rydberg atoms / machine learning

References

[1] D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, Synthetic three-dimensional atomic structures assembled atom by atom, Nature 561(7721), 79 (2018)

[2] H. Sun, Y. Song, A. Byun, H. Jeong, and J. Ahn, Imaging three-dimensional single-atom arrays all at once, Opt. Express 29(3), 4082 (2021)

[3] G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences, Rev. Mod. Phys.91(4), 045002 (2019)

[4] J. Lee, A. Seko, K. Shitara, K. Nakayama, and I. Tanaka, Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques, Phys. Rev. B 93(11), 115104 (2016)

[5] D. L. Deng, X. Li, and S. D. Das Sarma, Machine learning topological states, Phys. Rev. B 96(19), 195145 (2017)

[6] K. Min, B. Choi, K. Park, and E. Cho, Machine learning assisted optimization of electrochemical properties for Nirich cathode materials, Sci. Rep. 8(1), 15778 (2018)

[7] G. Torlai, G. Mazzola, J. Carrasquilla, M. Troyer, R. Melko, and G. Carleo, Neural-network quantum state tomography, Nat. Phys. 14(5), 447 (2018)

[8] T. Weiss and O. Romero-Isart, Quantum motional state tomography with nonquadratic potentials and neural networks, Phys. Rev. Res. 1(3), 033157 (2019)

[9] Y. Che, C. Gneiting, T. Liu, and F. Nori, Topological quantum phase transitions retrieved through unsupervised machine learning, Phys. Rev. B 102(13), 134213 (2020)

[10] A. J. Barker, H. Style, K. Luksch, S. Sunami, D. Garrick, F. Hill, C. J. Foot, and E. Bentine, Applying machine learning optimization methods to the production of a quantum gas, Mach. Learn.: Sci. Technol. 1(1), 015007 (2020)

[11] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, and J. Vanderplas, Scikit-learn: Machine learning in python, J. Mach. Learn. Res.12, 2825 (2011)

[12] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole blockade and quantum information processing in mesoscopic atomic ensembles, Phys. Rev. Lett. 87(3), 037901 (2001)

[13] M. Kim, Y. Song, J. Kim, and J. Ahn, Quantum Ising Hamiltonian programming in trio, quartet, and sextet qubit systems, PRX Quantum 1(2), 020323 (2020)

[14] E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, Observation of Rydberg blockade between two atoms, Nat. Phys. 5(2), 110 (2009)

[15] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Observation of collective excitation of two individual atoms in the Rydberg blockade regime, Nat. Phys. 5(2), 115 (2009)

[16] A. Géron, Hands-On Machine Learning with Scikit-Learn, Keras & Tensor Flow, O’Reilly Media, 2019

[17] D. Cox and D. Hinkley, Theoretical Statistics, Chapman & Hall, 1974

[18] R. Hoekstra, R. D. Morey, J. N. Rouder, and E. J. Wagenmakers, Robust misinterpretation of confidence intervals, Psychon. Bull. Rev.21(5), 1157 (2014)

[19] L. D. Brown, T. T. Cai, and A. DasGupta, Interval estimation for a binomial proportion, Stat. Sci. 16(2), 101 (2001)

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