Related papers: Adaptive Patching for Tensor Train Computations

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…

We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…

We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…

The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor…

Quantization is commonly used in Deep Neural Networks (DNNs) to reduce the storage and computational complexity by decreasing the arithmetical precision of activations and weights, a.k.a. tensors. Efficient hardware architectures employ…

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…

Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…

Qubit Mapping is a critical task in Quantum Compilation, as modern Quantum Processing Units (QPUs) are constrained to nearest-neighbor interactions defined by a qubit coupling graph. This compiler pass repairs the connectivity of two-qubit…

Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature has focused on devising accurate numerical integration…

We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…

The point cloud learning community witnesses a modeling shift from CNNs to Transformers, where pure Transformer architectures have achieved top accuracy on the major learning benchmarks. However, existing point Transformers are…

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success…

We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms…

The adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground state energy calculation, yet its practical scalability is hampered by…

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…

A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…

Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…

Quantization Aware Training (QAT) is a neural network quantization technique that compresses model size and improves operational efficiency while effectively maintaining model performance. The paradigm of QAT is to introduce fake…

As machine learning inferences increasingly move to edge devices, adapting to diverse computational capabilities, hardware, and memory constraints becomes more critical. Instead of relying on a pre-trained model fixed for all future…

Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…