Identifying quantum phase transitions using artificial neural networks on experimental data

Abstract

Machine learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications. Here we employ an artificial neural network and deep learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results, which were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model and provide an accurate characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose-Hubbard system. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known.Ultracold quantum gases have established as a formidable experimental platform to study paradigmatic quantum many-body systems in a well-controlled environment (1, 2). Important break-throughs include the realization of paradigmatic condensed matter models such as the Mott insulator transition or topological quantum matter. While these systems offer complementary observables to solid state systems, finding proper observables for quantum phases remains a key challenge, in particular in exotic systems such as non-local topological order of many-body localization. Here we explore a new approach building on modern machine learning techniques (3). Inspired by the success of convolutional neural networks in image recognition, we feed such networks with single images of momentum-space density, which are a standard experimental output of quantum gas experiments. We train it on large data sets of labelled images taken far away from the phase transition and apply the trained network to test data across the phase transition. The network is able to identify the correct position of the phase transition in parameter space from single experimental images. This is crucial advance for optimizing parameters, because the phase can now be determined from single images for direct decisions in the laboratory, and points towards future fully automated quantum simulators. We expect these techniques to be valuable also for in-situ snapshots as captured by quantum gas microscopes (4, 5). Similar approaches were previously applied to numerical Monte Carlo simulations of various physical models (6)(7)(8)(9)(10)(11)(12)(13). Neural networks are also opening new avenues in other areas of quantum physics, such as the representation of quantum many-body states (14,15) or the optimization of complex systems (16)(17)(18).We demonstrate the power of artificial neural networks on two physical examples, namely the topological phase transition in the Haldane model and the superfluid-to-Mott-insulator transition in the Bose-Hubbard model, both realized for cold atoms in optical lattices. We show that we can perform tasks, which were not possible with conventional techniques, such as the determination of non-local topological order from a sing...

Integrating Neural Networks with a Quantum Simulator for State Reconstruction

“…Neural network-based machine learning has recently emerged as a powerful technique for learning compact representations of high-dimensional data [10][11][12]. In experimental quantum science, these tools have already been applied profitably to the classification of experimental snapshots [13,14] and qubit readout [15]. The same data-driven approach can be applied to tomographic tasks.…”

Application of machine learning approach in disordered materials

“…此外, 机器学习还被用来 研究量子体系. 例如, 利用人工神经网络识别量子相 变 [16] ; 利用深度神经网络预测和开发量子拓扑材料 [17] , 将机器学习与量子计算相结合进行电子结构计算 [18] , 并且发展了量子机器学习算法以解决量子计算中编码 问题 [19] 等方面的研究. 由此可见 [20,21] 、分子动 力学模拟 [22,23] 以及蒙特卡罗方法.…”

Unsupervised learning using topological data augmentation

“…Artificial neural networks (NNs), one of the most efficient and widely used tools of ML [8], are currently at the frontier of research activity. It has been shown that they are capable of predicting phase transitions and critical temperatures [9][10][11][12][13][14][15][16][17][18][19], learning topological indices of quantum phases [20][21][22][23][24][25][26], efficiently representing many-body states [27][28][29][30][31][32][33][34], improving known numerical computational methods [35][36][37], and decoding topological quantum correcting codes [38][39][40][41][42].…”