The impressive progress in quantum hardware of the last years has raised the interest of the
quantum computing community in harvesting the computational power of such devices …

We consider two related tasks:(a) estimating a parameterisation of a given Gibbs state and
expectation values of Lipschitz observables on this state;(b) learning the expectation values …

We propose a generalization of the Wasserstein distance of order 1 to the quantum states of
n qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis …

We derive geometrical bounds on the irreversibility in both quantum and classical Markovian
open systems that satisfy the detailed balance condition. Using information geometry, we …

Estimating physical properties of quantum states from measurements is one of the most
fundamental tasks in quantum science. In this work, we identify conditions on states under …

We propose a new generalization to quantum states of the Wasserstein distance, which is a
fundamental distance between probability distributions given by the minimization of a …

We study dynamical optimal transport metrics between density matrices associated to
symmetric Dirichlet forms on finite-dimensional C^* C∗-algebras. Our setting covers …

We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional
matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we …

Quantifying how far the output of a learning algorithm is from its target is an essential task in
machine learning. However, in quantum settings, the loss landscapes of commonly used …

Given a uniform, frustration-free family of local Lindbladians defined on a quantum lattice
spin system in any spatial dimension, we prove a strong exponential convergence in relative …