6 papers
Renormalization flows for 1D mixed states and a quantum Goursat lemma
Léo Le-Nestour, David Pérez-GarcÃa, Alberto Ruiz-de-Alarcón
Renormalization provides a framework for relating microscopic models of physical systems to effective descriptions at larger length scales. This procedure is studied for the bounda…
The product structure of MPS-under-permutations
Marta Florido-Llinà s, Ãlvaro M. Alhambra, Rahul Trivedi +3
Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such…
Tensorization of neural networks for improved privacy and interpretability
José Ramón Pareja Monturiol, Alejandro Pozas-Kerstjens, David Pérez-GarcÃa
We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The…
Parent Lindbladians for Matrix Product Density Operators
Yuhan Liu, Alberto Ruiz-de-Alarcón, Georgios Styliaris +3
Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, w…
Undecidability in Physics: a Review
Ãlvaro Perales-Eceiza, Toby Cubitt, Mile Gu +2
The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is…
Spectral Gap Bounds for Quantum Markov Semigroups via Correlation Decay
Angelo Lucia, David Pérez-GarcÃa, Antonio Pérez-Hernández
Starting from an arbitrary full-rank state of a lattice quantum spin system, we define a "canonical purified Hamiltonian" and characterize its spectral gap in terms of a spatial mi…