Related papers: Quantum Optimal Transport: Quantum Channels and Qu…
Unprecedented control over the manufacture of electronic devices on nanometer scale has allowed to perform highly controllable and fine-tuned experiments in the quantum regime where exotic effects can nowadays be measured. In quantum dot…
Quantum transport is the study of the motion of electrons through nano-scale structures small enough that quantum effects are important. In this contribution I review recent theoretical proposals to use the techniques of quantum feedback…
Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density,…
Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of quantum classifier, based on quantum…
These lecture notes present the quantitative harmonic approximation result for quadratic optimal transport and general measures obtained by Goldman and Otto. The aim is to give a clear presentation of the proof of the main theorem with more…
Quantum computing, leveraging the principles of quantum mechanics, has been found to significantly enhance computational capabilities in principle, in some cases beyond classical computing limits. This paper explores quantum computing's…
This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open…
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, and more generally the classical Wasserstein distance…
Currently, quantum reservoir computing is one of the most promising and experimentally accessible techniques for hybrid, quantum-classical machine learning. However, its applications are limited due to practical restrictions on the size of…
We model one-dimensional transport through each open channel of a quantum wire by a Luttinger liquid with three different interaction parameters for the leads, the contact regions and the wire, and with two barriers at the contacts. We show…
We introduce quantum optimal transport of states on tracial AF-$C^{*}$-algebras to study non-spatial transport of quantum information, and view it as the pointwise case of a general parametrised one. We define quantum optimal transport…
We establish the optimal quantum teleportation protocol for the realistic scenario when both input state and quantum channel are afflicted by noise. In taking these effects into account higher fidelities are achieved. The optimality of the…
Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. We report teleportation of quantum…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…
Transport properties play a crucial role in several fields of science, as biology, chemistry, sociology, information science, and physics. The behavior of many dynamical processes running over complex networks is known to be closely related…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
A protocol of quantum communication is proposed in terms of the multi-qubit quantum teleportation through cluster states (Phys. Rev. Lett. \textbf{86}, 910 (2001)). Extending the cluster state based quantum teleportation on the basic unit…
We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
The presentation covers prerequisite results from Topology and Measure Theory. This is then followed by an introduction into couplings and basic definitions for optimal transport. The Kantrorovich problem is then introduced and an existence…