Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

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 …

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 unitary transformation, what is the size of the smallest quantum circuit that
implements it? This quantity, known as the quantum circuit complexity, is a fundamental …

Quantum functional inequalities (eg, the logarithmic Sobolev and Poincaré inequalities)
have found widespread application in the study of the behavior of primitive quantum Markov …

The Wasserstein metric is broadly used in optimal transport for comparing two probabilistic
distributions, with successful applications in various fields such as machine learning, signal …

We consider the problem of devising suitable quantum error correction (QEC) procedures for
a generic quantum noise acting on a quantum circuit. In general, there is no analytic …

We extend our previous work on a biologically inspired dynamic Monge–Kantorovich model
(Facca et al. in SIAM J Appl Math 78: 651–676, 2018) and propose it as an effective tool for …

We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a
particular type of optimal transport distance with transport cost homogeneous of degree one …

Classical shadows constitute a protocol to estimate the expectation values of a collection of
M observables acting on O (1) qubits of an unknown n-qubit state with a number of …