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We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.
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In this work, we characterize the performance of a deep convolutional neural network designed to detect and quantify chemical elements in experimental X-ray photoelectron spectroscopy data. Given the lack of a reliable database in literature, in order to train the neural network we computed a large ($>$100 k) dataset of synthetic spectra, based on randomly generated materials covered with a layer of adventitious carbon. The trained net performs as good as standard methods on a test set of $approx$ 500 well characterized experimental X-ray photoelectron spectra. Fine details about the net layout, the choice of the loss function and the quality assessment strategies are presented and discussed. Given the synthetic nature of the training set, this approach could be applied to the automatization of any photoelectron spectroscopy system, without the need of experimental reference spectra and with a low computational effort.
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that had previously been intractable for existing exact numerical methods. Here, we demonstrate the utility of the variational representation of quantum states based on artificial neural networks for performing quantum optimization. We show empirically that this methodology achieves high approximation ratio solutions with polynomial classical computing resources for a range of instances of the Maximum Cut (MaxCut) problem whose solutions have been encoded into the ground state of quantum many-body systems up to and including 256 qubits.
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution of the distribution of the local fields and, hence, the evolution of the order parameters. A comparison of this approach is made with the generating functional method, allowing to calculate any physical relevant quantity as a function of time. Explicit analytic formula are given in both methods for the first few time steps of the dynamics. Up to the third time step the results are identical. Some arguments are presented why beyond the third time step the results differ for certain values of the model parameters. Furthermore, fixed-point equations are derived in the stationary limit. Numerical simulations confirm our theoretical findings.
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system utilizing the benefits of artificial neural network. Without assuming the specific forms of the eigenvectors, this algorithm can find the eigenvectors in an unbiased way with well controlled accuracy. As examples, we apply this algorithm to 1D Ising and Heisenberg models, where the results match very well with exact diagonalization.
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.
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