arXiv subjects

Juan José Rodríguez-Aldavero

Publications and source records attributed to Juan José Rodríguez-Aldavero.

3 recordsLinked to original sources

arXiv2026

Approximation and composition of functions in quantized tensor trains via orthogonal polynomial expansions

This work explores the representation of univariate and multivariate functions as quantized tensor trains (QTT). It develops a constructive algorithm that employs expansions in orthogonal polynomial bases and Clenshaw evaluations to represent analytic and highly differentiable functions as QTT approximants. This approach provides a general framework for function composition in QTT form that generalizes efficiently to multidimensional settings. Without loss of generality, the presentation focuses on the Chebyshev basis, where the method demonstrates rapid convergence for highly differentiable functions, in agreement with classical theoretical predictions, and remains numerically stable at high polynomial orders. The performance of the algorithm is compared with that of tensor cross-interpolation (TCI) and multiscale interpolative constructions, demonstrating competitive performance and favorable scaling behavior in certain scenarios.

quant-ph↗

arXiv2026

SeeMPS: A Python-based Matrix Product State and Tensor Train Library

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision linear algebra package where exponentially large vector spaces are compressed using the MPS/TT formalism. It enables both low-level operations, such as vector addition, linear transformations, and Hadamard products, as well as high-level algorithms, including the approximation of linear equations, eigenvalue computations, and exponentially efficient Fourier transforms. This library can be used for traditional quantum many-body physics applications and also for quantum-inspired numerical analysis problems, such as solving PDEs, interpolating and integrating multidimensional functions, sampling multivariate probability distributions, etc.

quant-ph↗

arXiv2026

High-Resolution Tensor-Network Fourier Methods for Exponentially Compressed Non-Gaussian Aggregate Distributions

Characteristic functions of weighted sums of independent random variables exhibit low-rank structure in the quantized tensor train (QTT) representation, also known as matrix product states (MPS), enabling up to exponential compression of their fully non-Gaussian probability distributions. Under variable independence, the global characteristic function factorizes into local terms. Its low-rank QTT structure arises from intrinsic spectral smoothness in continuous models, or from spectral energy concentration as the number of components $D$ grows in discrete models. We demonstrate this on weighted sums of Bernoulli and lognormal random variables. In the former, despite an adversarial, incompressible small-$D$ regime, the characteristic function undergoes a sharp bond-dimension collapse for $D \gtrsim 300$ components, enabling polylogarithmic time and memory scaling. In the latter, the approach reaches high-resolution discretizations of $N = 2^{30}$ frequency modes on standard hardware, far beyond the $N = 2^{24}$ ceiling of dense implementations. These compressed representations enable efficient computation of Value at Risk (VaR) and Expected Shortfall (ES), supporting applications in quantitative finance and beyond.

stat.ML↗