Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its generalization and extrapolation capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in extrapolating its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.
Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its generalization and extrapolation capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in extrapolating its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.
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.
Abstract Deep neural networks have demonstrated remarkable efficacy in extracting meaningful representations from complex datasets. This has propelled representation learning as a compelling area of research across diverse fields. One interesting open question is how beneficial representation learning can be for quantum many-body physics, with its notoriously high-dimensional state space. In this work, we showcase the capacity of a neural network that was trained on a subset of physical observables of a many-body system to partially acquire an implicit representation of the wave function. We illustrate this by demonstrating the effectiveness of reusing the representation learned by the neural network to enhance the learning process of another quantity derived from the quantum state. In particular, we focus on how the pre-trained neural network can enhance the learning of entanglement entropy. This is of particular interest as directly measuring the entanglement in a many-body system is very challenging, while a subset of physical observables can be easily measured in experiments. We show the pre-trained neural network learns the dynamics of entropy with fewer resources and higher precision in comparison with direct training on the entanglement entropy.
Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data. Previous experimental demonstrations in this paradigm, however, have largely been limited to small systems or highly structured states, due to the difficulty of preparing many-body ground states on quantum processors. In this work, we demonstrate learning from experimental quantum data generated from approximate ground states of the two-dimensional Heisenberg XXZ model with system sizes up to 115 qubits. We construct a dataset of single-site expectation values, two-point correlations, and 12-body loop correlations across the antiferromagnetic phase. We then train neural networks on this data and show that they can accurately predict spatially resolved observables for previously unseen Hamiltonian parameters, both within the training distribution and in an out-of-distribution regime approaching the phase boundary. Our results demonstrate the practical realization of learning from quantum data for an interacting two-dimensional many-body system at scale, motivating a path toward regimes where quantum processors could provide training data beyond the reach of classical approximation methods.
In the past decades, methods to solve the ground state given a quantum many-body Hamiltonian have been well established. In this work, we consider an inverse problem and demonstrate that convolutional neural network (CNN) can predict the physical parameters of interacting Hamiltonians, such as coupling strengths and magnetic fields, providing the quantum many-body wave-functions as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately predict the parameters of the states beyond such training regions. For instance, our results show that QubismNet can predict the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations.
Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, previous studies have demonstrated inevitable trainability issues that severely limit their capabilities in the large-scale regime. In this work, we propose a quantum recurrent embedding neural network (QRENN) inspired by fast-track information pathways in ResNet and general quantum circuit architectures in quantum information theory. By employing dynamical Lie algebras, we provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus. Notably, the general QRENN architecture resists classical simulation as it encompasses powerful quantum circuits such as QSP, QSVT, and DQC1, which are widely believed to be classically intractable. Building on this theoretical foundation, we apply our QRENN to accurately classify quantum Hamiltonians and detect symmetry-protected topological phases, demonstrating its applicability in quantum supervised learning. Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning in predicting physical properties and solving complex problems.
The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information-a quantity recently developed to characterize information scrambling-to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.