Quantum approximated cloning-assisted density matrix exponentiation

Abstract

Publisher Copyright: © 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.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 (LMR) protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal setup, and in a realistic scenario, the copies are limited and the noncloning theorem prevents one 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.Peer reviewe