Quantum approximated cloning-assisted density matrix exponentiation

Understand

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.