Related papers: Storage capacity and learning capability of quantu…

In this study we employ a feed-forward artificial neural network (FFNN) architecture to perform tomography of quantum states and processes obtained from noisy experimental data. To evaluate the performance of the FFNN, we use a heavily…

Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…

Quantum Machine Learning continues to be a highly active area of interest within Quantum Computing. Many of these approaches have adapted classical approaches to the quantum settings, such as QuantumFlow, etc. We push forward this trend and…

Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage…

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

The storage capacity of a binary classification model is the maximum number of random input-output pairs per parameter that the model can learn. It is one of the indicators of the expressive power of machine learning models and is important…

In existing image classification systems that use deep neural networks, the knowledge needed for image classification is implicitly stored in model parameters. If users want to update this knowledge, then they need to fine-tune the model…

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…

Quantum computers require precise control over parameters and careful engineering of the underlying physical system. In contrast, neural networks have evolved to tolerate imprecision and inhomogeneity. Here, using a reservoir computing…

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden…

Inspired by the dissipative quantum model of brain, we model the states of neural nets in terms of collective modes by the help of the formalism of Quantum Field Theory. We exhibit an explicit neural net model which allows to memorize a…

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…

Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces…

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the…

In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…

In this paper, we address the problem of reducing the memory footprint of convolutional network architectures. We introduce a vector quantization method that aims at preserving the quality of the reconstruction of the network outputs rather…

Quantum neural networks (QNNs) leverage quantum entanglement and superposition to enable large-scale parallel linear computation, offering a potential solution to the scalability limits of classical deep learning. However, their practical…

The past few years have seen a surge in the application of quantum theory methodologies and quantum-like modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various…