Deep Learning of Quantum Many-Body Dynamics via Random Driving

Naeimeh Mohseni1,2, Thomas Fösel1,2, Lingzhen Guo1, Carlos Navarrete-Benlloch1,3,4, and Florian Marquardt1,2

1Max-Planck-Institut für die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany
2Physics Department, University of Erlangen-Nuremberg, Staudtstr. 5, 91058 Erlangen, Germany
3Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
4Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

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Abstract

Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is $\textit{based purely on monitoring expectation values of observables under random driving}$. The trained recurrent network is able to produce accurate predictions for driving trajectories entirely different than those observed during training. As a proof of principle, here we train the network on numerical data generated from spin models, showing that it can learn the dynamics of observables of interest without needing information about the full quantum state. This allows our approach to be applied eventually to actual experimental data generated from a quantum many-body system that might be open, noisy, or disordered, without any need for a detailed understanding of the system. This scheme provides considerable speedup for rapid explorations and pulse optimization. Remarkably, we show the network is able to extrapolate the dynamics to times longer than those it has been trained on, as well as to the infinite-system-size limit.

One of the main outstanding challenges in quantum physics is an efficient treatment of nonequilibrium dynamics in quantum many-body systems. Direct simulations are constrained by the need to evolve the exponentially large many-body wave function, while ansatz solutions (including modern techniques like matrix product states) are typically restricted in their applicability. In this work, we introduce a novel approach to tackle this challenge, based on deep neural networks.

In contrast to the previous attempts to employ neural networks to represent variational wave functions, we entirely forego the need to deal with the quantum state itself. Rather, we show that we can teach a neural network to predict the nonequilibrium dynamics of a many-body quantum system, by having it observe the dynamics of a selected subset of degrees of freedom under random driving.

Being able to learn the dynamics by partial observations, without requiring information about the full state makes our scheme of high potential practical relevance. In particular, it immediately recommends itself to future applications in experiments where a full quantum-state tomography would be infeasible. In such cases, the network can be trained on experimental data without any knowledge of the underlying model. An independent benefit of our scheme is the significant speedup that could be used for certain tasks, e.g., for pulse engineering. The clear benefits arising from our scheme and the relative simplicity of the implementation make it a very promising approach for the prediction of quantum many-body dynamics.

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[1] Yaroslav Kharkov, Oles Shtanko, Alireza Seif, Przemyslaw Bienias, Mathias Van Regemortel, Mohammad Hafezi, and Alexey V. Gorshkov, "Discovering hydrodynamic equations of many-body quantum systems", arXiv:2111.02385.

[2] Naeimeh Mohseni, Carlos Navarrete-Benlloch, Tim Byrnes, and Florian Marquardt, "Deep recurrent networks predicting the gap evolution in adiabatic quantum computing", arXiv:2109.08492.

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