Deep Learning of Quantum Many-Body Dynamics via Random Driving

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 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.

Deep learning of many-body observables and quantum information scrambling

“…The neural network provides as output the desired observables for the considered circuit depth, see Ref. [18] for more details about LSTM architecture and how it decides the flow of information in and out at each step. We always start from a product state where all qubits are prepared in the +1 eigenstate of the σ z operator.…”

“…Classical machine learning algorithms have exhibited an impressive ability to find high-accuracy approximations for desired quantities of quantum many-body systems, especially for problems that do not permit numerically exact solutions [12][13][14]. In particular, the challenging task of computing real-time-evolutions of many-body dynamics has been addressed using both data-driven learning methods [15][16][17][18] and direct calculation methods such as reinforcement learning. Especially for the latter, the neural network wave function ansatz [14,19,20], where neural networks find an efficient representation for the wave function, has entailed large interest.…”

Learning Quantum Systems

“…Other methods exploit NNs to generalise QPT to the characterisation of time dependent spin systems [139], while yet another class reconstructs a unitary quantum process by inverting the dynamics using a variational algorithm [140,141]. RNNs have recently been shown to be useful in learning the non-equilibrium dynamics of a many-body quantum system from its nonlinear response under random driving [142].…”

Artificial Intelligence and Machine Learning for Quantum Technologies

“…In [53], the authors show how a recurrent neural network [24] can approximate the properties that emerge from quantum experiments without ever storing the intermediate quantum state directly. These systems could then directly be applied for complex quantum design tasks, a topic we cover in chapter III D. Another approach [54] also foregoes the representation of quantum states and instead trains a recurrent network to predict the evolution of observables under random external driving of a quantum many-body system (either based on simulated or possibly even experimental data). The trained network can then predict the evolution under arbitrary driving patterns (e.g.…”