1
|
Costa E, Scriva G, Fazio R, Pilati S. Deep-learning density functionals for gradient descent optimization. Phys Rev E 2022; 106:045309. [PMID: 36397567 DOI: 10.1103/physreve.106.045309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid them by using an ad hoc convolutional architecture featuring an interchannel averaging layer. The main testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the interchannel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.
Collapse
Affiliation(s)
- E Costa
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - G Scriva
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - R Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Napoli, Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| |
Collapse
|
2
|
Quantum Reservoir Computing for Speckle Disorder Potentials. CONDENSED MATTER 2022. [DOI: 10.3390/condmat7010017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed.
Collapse
|
3
|
Seo S, Lee JH, Lee SB, Park SE, Seo MH, Park J, Kwon TY, Hong HG. Maximized atom number for a grating magneto-optical trap via machine-learning assisted parameter optimization. OPTICS EXPRESS 2021; 29:35623-35639. [PMID: 34808993 DOI: 10.1364/oe.437991] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 10/07/2021] [Indexed: 06/13/2023]
Abstract
We present a parameter set for obtaining the maximum number of atoms in a grating magneto-optical trap (gMOT) by employing a machine learning algorithm. In the multi-dimensional parameter space, which imposes a challenge for global optimization, the atom number is efficiently modeled via Bayesian optimization with the evaluation of the trap performance given by a Monte-Carlo simulation. Modeling gMOTs for six representative atomic species - 7Li, 23Na, 87Rb, 88Sr, 133Cs, 174Yb - allows us to discover that the optimal grating reflectivity is consistently higher than a simple estimation based on balanced optical molasses. Our algorithm also yields the optimal diffraction angle which is independent of the beam waist. The validity of the optimal parameter set for the case of 87Rb is experimentally verified using a set of grating chips with different reflectivities and diffraction angles.
Collapse
|
4
|
Miles C, Bohrdt A, Wu R, Chiu C, Xu M, Ji G, Greiner M, Weinberger KQ, Demler E, Kim EA. Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data. Nat Commun 2021; 12:3905. [PMID: 34162847 PMCID: PMC8222395 DOI: 10.1038/s41467-021-23952-w] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 05/27/2021] [Indexed: 11/09/2022] Open
Abstract
Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data.
Collapse
Affiliation(s)
- Cole Miles
- Department of Physics, Cornell University, Ithaca, NY, USA
| | - Annabelle Bohrdt
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics and Institute for Advanced Study, Technical University of Munich, Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), München, Germany
| | - Ruihan Wu
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Christie Chiu
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
- Princeton Center for Complex Materials, Princeton University, Princeton, NJ, USA
| | - Muqing Xu
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Eun-Ah Kim
- Department of Physics, Cornell University, Ithaca, NY, USA.
| |
Collapse
|
5
|
Guo S, Fritsch AR, Greenberg C, Spielman IB, Zwolak JP. Machine-learning enhanced dark soliton detection in Bose-Einstein condensates. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021; 2:10.1088/2632-2153/abed1e. [PMID: 36733297 PMCID: PMC9890383 DOI: 10.1088/2632-2153/abed1e] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023] Open
Abstract
Most data in cold-atom experiments comes from images, the analysis of which is limited by our preconceptions of the patterns that could be present in the data. We focus on the well-defined case of detecting dark solitons-appearing as local density depletions in a Bose-Einstein condensate (BEC)-using a methodology that is extensible to the general task of pattern recognition in images of cold atoms. Studying soliton dynamics over a wide range of parameters requires the analysis of large datasets, making the existing human-inspection-based methodology a significant bottleneck. Here we describe an automated classification and positioning system for identifying localized excitations in atomic BECs utilizing deep convolutional neural networks to eliminate the need for human image examination. Furthermore, we openly publish our labeled dataset of dark solitons, the first of its kind, for further machine learning research.
Collapse
Affiliation(s)
- Shangjie Guo
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Amilson R Fritsch
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Craig Greenberg
- National Institute of Standards and Technology, Gaithersburg, MD 20899, United States of America
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Justyna P Zwolak
- National Institute of Standards and Technology, Gaithersburg, MD 20899, United States of America,Author to whom any correspondence should be addressed.
| |
Collapse
|
6
|
Saraceni N, Cantori S, Pilati S. Scalable neural networks for the efficient learning of disordered quantum systems. Phys Rev E 2020; 102:033301. [PMID: 33075937 DOI: 10.1103/physreve.102.033301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 08/11/2020] [Indexed: 12/20/2022]
Abstract
Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [Mills et al., Chem. Sci. 10, 4129 (2019)2041-652010.1039/C8SC04578J] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely, a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pretraining performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.
Collapse
Affiliation(s)
- N Saraceni
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| | - S Cantori
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| |
Collapse
|
7
|
Moreno JR, Carleo G, Georges A. Deep Learning the Hohenberg-Kohn Maps of Density Functional Theory. PHYSICAL REVIEW LETTERS 2020; 125:076402. [PMID: 32857556 DOI: 10.1103/physrevlett.125.076402] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 07/14/2020] [Indexed: 06/11/2023]
Abstract
A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning nonsmooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.
Collapse
Affiliation(s)
- Javier Robledo Moreno
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Center for Quantum Phenomena, Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA
| | - Giuseppe Carleo
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Antoine Georges
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- CPHT, CNRS, École Polytechnique, IP Paris, F-91128 Palaiseau, France
- DQMP, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Suisse
| |
Collapse
|