Related papers: Double descent: When do neural quantum states gene…
Exponential complexity of many-body wave functions limits accurate numerical simulations of real-time dynamics, especially beyond 1D, where rapid entanglement growth poses severe challenges. Neural Quantum States (NQS) have emerged as a…
Quantum computers have the potential to revolutionize diverse fields, including quantum chemistry, materials science, and machine learning. However, contemporary quantum computers experience errors that often cause quantum programs run on…
A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…
Projected variational wavefunctions such as the Gutzwiller, many-body correlator and Jastrow ansatzes have provided crucial insight into the nature of superfluid-Mott insulator transition in the Bose Hubbard model (BHM) in two or more…
The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly…
The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small…
Deep classifier neural networks enter the terminal phase of training (TPT) when training error reaches zero and tend to exhibit intriguing Neural Collapse (NC) properties. Neural collapse essentially represents a state at which the…
Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…
Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that…
It has been proven that, compared to using 32-bit floating-point numbers in the training phase, Deep Convolutional Neural Networks (DCNNs) can operate with low precision during inference, thereby saving memory space and power consumption.…
Recently, significant progress has been made in understanding the generalization of neural networks (NNs) trained by gradient descent (GD) using the algorithmic stability approach. However, most of the existing research has focused on…
Quantum many-body problems are some of the most challenging problems in science and are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial…
Learning probability distribution is an essential framework in classical learning theory. As a counterpart, quantum state learning has spurred the exploration of quantum machine learning theory. However, as dimensionality increases,…
Neural collapse (NC) and its multi-layer variant, deep neural collapse (DNC), describe a structured geometry that occurs in the features and weights of trained deep networks. Recent theoretical work by Sukenik et al. using a deep…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
Image classification is a fundamental computer vision problem, and neural networks offer efficient solutions. With advancing quantum technology, quantum neural networks have gained attention. However, they work only for low-dimensional data…
It has been observed by Belkin et al.\ that over-parametrized neural networks exhibit a `double descent' phenomenon. That is, as the model complexity (as reflected in the number of features) increases, the test error initially decreases,…
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of…