Learning quantum dynamics with latent neural ODEs

Deep learning and neural networks have recently become the powerhouse in machine learning (ML) and they have successfully been used to tackle complex problems In general, the study of open quantum systems are in classical [1-3] and quantum mechanics [4-7] (see Refs. important for quantum computing as well as many [8-12] for reviews). Machine-assisted scientific discovery other areas of physics from many-body phenomenon [27, is still in its infancy but progress has been made, mostly 28], light-matter interaction [29-31] to non-equilibrium by building the correct inductive bias-or structure into physics [32, 33]. the model or loss function. For example physical conservation laws can be learned [1, 2]. Other work has made progress, in a purely data-driven approach learning relationships between quantum experiments and entanglement Here, we demonstrate that latent ODEs can be trained using generative models [13]. Recently, neural to generate and extrapolate measurement data from dynamical ordinary differential equations (ODEs) were introduced quantum evolution in both closed and open [14, 15], a neural network layer defined by differential quantum systems using only physical observations without equations. Neural ODEs provide the perfect model for specifying the physics a priori. This is in line with physics, since many physical laws are governed by ODEs, treating the quantum system as a black box and the "shut and thus every neural ODE has the correct inductive bias up and calculate" philosophy [34] all the while ignoring built into the model itself.