Learning quantum dynamics with latent neural ODEs

Abstract

The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counter-intuitive nature of quantum mechanics. Here, we present the QNODE, a latent neural ODE trained on expectation values of closed and open quantum systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems respectively in an unsupervised means. Furthermore, the QNODE rediscovers quantum mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.

arXiv comment11 Pages. 8 Figures. This is a resubmission. We added more results and plots for more quantitative analysis

References in corpus (26)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• Variational Quantum Algorithms
• Machine learning and the physical sciences
• Quantum computational advantage using photons
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Dynamical Decoupling of Open Quantum Systems
• Noisy intermediate-scale quantum (NISQ) algorithms
• Machine learning phases of matter
• Strong quantum computational advantage using a superconducting quantum processor
• Explainable Machine Learning for Scientific Insights and Discoveries
• Many-body quantum state tomography with neural networks
• Dynamical quantum phase transitions: a review
• Discovering physical concepts with neural networks
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Machine learning meets quantum physics
• Multiparameter optimisation of a magneto-optical trap using deep learning
• Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations
• Quantum phenomena modelled by interactions between many classical worlds
• Machine Learning meets Quantum Foundations: A Brief Survey
• Dynamical quantum phase transitions and non-Markovian dynamics
• Creation of quantum error correcting codes in the ultrastrong coupling regime
• Quantum Computer-Aided design of Quantum Optics Hardware
• Quantum computer-aided design: digital quantum simulation of quantum processors
• Floquet stroboscopic divisibility in non-Markovian dynamics

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• QD3SET-1: A Database with Quantum Dissipative Dynamics Data Sets
• Characterization of a driven two-level quantum system by Supervised Learning
• Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations