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Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…

Many recent machine learning tasks resort to quantum computing to improve classification accuracy and training efficiency by taking advantage of quantum mechanics, known as quantum machine learning (QML). The variational quantum circuit…

This paper proposes a fundamentally new paradigm for image generation through set-based tokenization and distribution modeling. Unlike conventional methods that serialize images into fixed-position latent codes with a uniform compression…

We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format which aims for numerical modeling of the 3D long-range interaction potentials in multi-particle systems. The main idea of the RS tensor format is the…

We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for…

There is an emerging interest in tensor factorization applications in big-data analytics and machine learning. To speed up the factorization of extra-large datasets, organized in multidimensional arrays (aka tensors), easy to compute…

The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few…

With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which…

Recently, data-driven methods have shown great promise for discovering governing equations from simulation or experimental data. However, most existing approaches are limited to scalar equations, with few capable of identifying tensor…

Large Language Models (LLMs) have shown immense potential in Knowledge Graph Completion (KGC), yet bridging the modality gap between continuous graph embeddings and discrete LLM tokens remains a critical challenge. While recent…

Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient…

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Inference for state-of-the-art deep neural networks is computationally expensive, making them difficult to deploy on constrained hardware environments. An efficient way to reduce this complexity is to quantize the weight parameters and/or…

We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network…

Although neural sequence-to-sequence models have been successfully applied to semantic parsing, they fail at compositional generalization, i.e., they are unable to systematically generalize to unseen compositions of seen components.…

Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…

Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this…