5 papers
Hankel and Multiplication Tensor Completions for Cactus Rank
Alessandra Bernardi, Joachim Jelisiejew, Oriol Reig Fité
We show that the Hankel flat extension formulation of the cactus algorithm is equivalent to a completion problem for multiplication tensors of Artinian Gorenstein algebras. The unk…
A quantum implementation of high-order power method for estimating geometric entanglement of pure states
Andrii Semenov, Niall Murphy, Simone Patscheider +2
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entang…
Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach
Paolo Andreini, Alessandra Bernardi, Monica Bianchini +4
Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, wh…
Triangular tensor networks, pencils of matrices and beyond
Alessandra Bernardi, Fulvio Gesmundo
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors…
A refinement on the local cactus rank algorithm
Alessandra Bernardi, Oriol Reig Fité
We present an algorithm to recover a minimal local apolar scheme to a homogeneous polynomial . The socle degree of the scheme determines whether it is evinced by a Generalized A…