7 papers
Unitaria: Quantum Linear Algebra via Block Encodings
Matthias Deiml, Oliver Hüttenhofer, Ram Mosco +2
We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on…
Constrained Optimal Polynomials for Quantum Linear System Solvers
Matthias Deiml, Daniel Peterseim
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation a…
Quantum Enhanced Numerical Homogenization
Loïc Balazi, Loïc Balazi, Matthias Deiml +1
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients that integrates classical coarse-scale solvers with quantum su…
Nonlinear quantum computation by amplified encodings
Matthias Deiml, Daniel Peterseim
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evalu…
Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients
Fabian Kröpfl, Daniel Peterseim, Elisabeth Ullmann
This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical h…
Quantum Sampling and Moment Estimation for Transformed Gaussian Random Fields
Matthias Deiml, Daniel Peterseim
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on -dimensional domains, based on an enhanced version of the classical moving average…