Quantum approximated cloning-assisted density matrix exponentiation

TL;DR

This paper introduces a quantum approximation method using cloning-assisted density matrix exponentiation to improve matrix embedding in quantum machine learning, especially when copies are limited.

Contribution

It proposes a novel approach that leverages imperfect quantum copies to enhance the Lloyd-Mohseni-Rebentrost protocol under realistic constraints.

Findings

Improved matrix exponentiation performance with imperfect copies.

Enhanced quantum embedding accuracy when eigenvectors are known.

Circumvents no-cloning limitations in quantum state copying.

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.