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arXiv:2203.10200 · Frontiers in Materials

Emulating quantum dynamics with neural networks via knowledge distillation

Yu Yao, Chao Cao, Stephan Haas, Mahak Agarwal, Divyam Khanna, Marcin Abram

Published Jan 4, 2023• 6 citations
arXivHTMLPDF

Abstract

We introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability by training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). We show that this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier), and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, we demonstrate, that using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure relative importance of the contributing physical processes.

DOI
10.3389/fmats.2022.1060744

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We introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability by training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). We show that this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier), and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, we demonstrate, that using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure relative importance of the contributing physical processes.
Quantum Neural Networks (QNNs) are a promising class of quantum machine learning models with potential quantum advantages when implemented on scalable, error-corrected quantum computers. However, as system sizes increase, deploying QNNs becomes challenging. Similar to their classical counterparts, a key obstacle to their practical applications is that large-scale QNNs may not be easily deployed on smaller systems that have limited resources. Here, we tackle this challenge by compressing QNNs via knowledge distillation. We demonstrate how well-trained QNNs on large systems can be distilled into smaller architectures with similar configurations. We numerically show that knowledge distillation helps reduce the training cost of QNNs in terms of the number of qubits and circuit depth. Additionally, we find that a self-knowledge-distillation approach can accelerate training convergence. We believe our results offer new strategies for the efficient compression and practical deployment of QNNs.
Knowledge distillation is a widely explored technique in classical machine learning, in which a smaller or more efficient model is trained to mimic the behavior of a larger, more complex model. In this study, we extend the concept of knowledge distillation from classical architectures to quantum architectures, with the goal of improving the training of quantum models while potentially reducing the number of parameters compared to their classical counterparts. Given the inherent challenges in training quantum neural networks, leveraging knowledge from well-established classical models could provide valuable insights and advantages, particularly in terms of model efficiency and performance. In this work we explore the potential benefits of this approach, evaluating a hybrid quantum model against a non-hybrid quantum baseline. While the proposed study is still in the preliminary stage, it aims to set the scene for further investigation into the most appropriate architecture for classical-to-quantum knowledge distillation in order to enhance the development and optimization of quantum neural networks more generally.
Abstract The emergence of classical behavior from quantum mechanics as Planck’s constant ℏ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and ℏ to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ∼ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as ℏ is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.
The rapid advancement of machine learning (ML) and the growing need for computational power have led to the exploration of quantum computing, which offers significant potential for faster complex calculations. However, Quantum Machine Learning (QML) faces challenges due to the limited number of qubits and noise of quantum circuits, particularly with Noisy Intermediate-Scale Quantum (NISQ) devices. These challenges severely limit the current capacity to train accurate and stable Quantum Machine Learning Models. In this paper, we propose a novel framework for QML that employs the knowledge distillation method to harness the power of well-trained classical machine learning (CML) models and enhance the training performance of QML models. In this framework, we utilize the well-trained CML as a teacher model to assist the training of the student QML model using the knowledge distillation method. By distilling knowledge from the robust CML model, our framework can potentially address the problem of the barren plateau which hinders effective model training. Knowledge distillation is well suited for this framework through the transfer of knowledge without parameter sharing. Through empirical tests, our framework has demonstrated not only an increase in the accuracy of QML models but also a notable improvement in training stability.
The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.
The classical limit of quantum mechanics, formally investigated through frameworks like strict deformation quantization, remains a profound area of inquiry in the philosophy of physics. This paper explores a computational approach employing a neural network to emulate the emergence of classical behavior from the quantum harmonic oscillator as Planck's constant ℏ\hbarℏ approaches zero. We develop and train a neural network architecture to learn the mapping from initial expectation values and ℏ\hbarℏ to the time evolution of the expectation value of position. By analyzing the network's predictions across different regimes of hbar, we aim to provide computational insights into the nature of the quantum-classical transition. This work demonstrates the potential of machine learning as a complementary tool for exploring foundational questions in quantum mechanics and its classical limit.