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Heuristic machinery to uncover hidden features of SU($N$) Fermions with neural networks

Entong Zhao, Jeongwon Lee, Chengdong He, Zejian Ren, Elnur Hajiyev, Junwei Liu, Gyu-Boong Jo

Published Jun 25, 2020• 0 citations
OpenAlex

Abstract

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with an unprecedented sensitivity. However, it still remains challenging to uncover hidden features directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by combining the power of ML and the trial and error in a supervised way. We use our machinery to reveal hidden thermodynamic features in the density profile of ultracold fermions interacting within SU($N$) spin symmetry prepared in a quantum simulator, and discover their connection to spin multiplicity. Although such spin symmetry should manifest itself in a many-body wavefuction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of $\sim$94$\%$ for detection of the spin multiplicity, we investigate the dependency of accuracy on various hidden features with filtered measurements. Guided by our machinery, we verify how the NN extracts a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU($N$) Fermi liquids, and to identify hidden features even for highly complex quantum matters with minimal prior understanding.

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Heuristic machinery to uncover hidden features of SU(NNN) Fermions with neural networks
The power of machine learning (ML) provides the possibility of analyzing experimental measurements with an unprecedented sensitivity. However, it still remains challenging to uncover hidden features directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by combining the power of ML and the trial and error in a supervised way. We use our machinery to reveal hidden thermodynamic features in the density profile of ultracold fermions interacting within SU(NNN) spin symmetry prepared in a quantum simulator, and discover their connection to spin multiplicity. Although such spin symmetry should manifest itself in a many-body wavefuction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ∼\sim∼94%\%% for detection of the spin multiplicity, we investigate the dependency of accuracy on various hidden features with filtered measurements. Guided by our machinery, we verify how the NN extracts a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU(NNN) Fermi liquids, and to identify hidden features even for highly complex quantum matters with minimal prior understanding.
The power of machine learning (ML) provides the possibility of analyzing experimental measurements with a high sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU(N) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefunction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ~94% for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU(N) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.
The power of machine learning (ML) provides the possibility of analyzing experimental measurements with a high sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU(N) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefunction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ~94% for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU(N) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.
Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in machine learning algorithms enable physicists to analyze experimental data with unprecedented high sensitivities, and identify quantum phases even in the presence of unavoidable noises. Here, we report a successful identification of topological phase transitions using a deep convolutional neural network trained with low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions. We apply the trained network to unseen data to map out a whole phase diagram, which predicts the positions of the two topological phase transitions that are consistent with the results obtained by using the conventional method on higher SNR data. By visualizing the filters and post-convolutional results of the convolutional layer, we further find that the CNN uses the same information to make the classification in the system as the conventional analysis, namely spin imbalance, but with an advantage concerning SNR. Our work highlights the potential of machine learning techniques to be used in various quantum systems.
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.
Machine Learning (ML) techniques have emerged as a powerful tool in quantum matter research. In this poster, we highlight how ML algorithms enable us to analyze experimental data with unprecedented high sensitivities and identify topological phases even in the presence of unavoidable noises. To this end, we apply the trained network to low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions [1]. The obtained phase diagram by ML is consistent with the results obtained by using the conventional method on higher SNR data. Our work highlights the potential of machine learning techniques to be used in various quantum systems.
Abstract Recent proposals have suggested the use of supervised learning with convolutional neural networks to shed light on some of the less well known phases of the Fermi-Hubbard model through the classification of snapshots from the quantum gas microscopy of ultracold atoms in optical lattices. However, there have been challenges in the interpretability of networks with more than one convolutional filter coupled to the input images. Here, we expand on previous work by considering multiple filters in the first convolutional layer and developing a process for analyzing the physical relevance of patterns obtained in the trained filters. We benchmark our approach at half-filling, where strong antiferromagnetic correlations are known to be present, and we find that upon hole doping, previously unknown patterns arise at temperatures below the tunneling amplitude. These patterns may be a signature of interesting arrangements of fermions in the lattice.