Quantum approximated cloning-assisted density matrix exponentiation
Abstract
Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation techniques enable the loading of matrices into quantum computers. A representative example of these methods is the Lloyd-Mohseni-Rebentrost protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal set up, and in a realistic scenario, the copies are limited and the non-cloning theorem prevents from producing more exact copies in order to increase the accuracy of the protocol. Here, we propose a method to circumvent this limitation by introducing imperfect quantum copies, which significantly improve the performance of the LMR when the eigenvectors are known.
Cite
@article{arxiv.2311.11751,
title = {Quantum approximated cloning-assisted density matrix exponentiation},
author = {Pablo Rodriguez-Grasa and Ruben Ibarrondo and Javier Gonzalez-Conde and Yue Ban and Patrick Rebentrost and Mikel Sanz},
journal= {arXiv preprint arXiv:2311.11751},
year = {2025}
}