Quantum approximated cloning-assisted density matrix exponentiation

• URL: http://arxiv.org/abs/2311.11751v2
• Date: Thu, 27 Mar 2025 08:12:31 GMT
• Title: Quantum approximated cloning-assisted density matrix exponentiation
• Authors: Pablo Rodriguez-Grasa, Ruben Ibarrondo, Javier Gonzalez-Conde, Yue Ban, Patrick Rebentrost, Mikel Sanz,
• Abstract summary: Hamiltonian simulation techniques enable the loading of matrices into quantum computers.<n>The Lloyd-Mohseni-Rebentrost protocol efficiently implements matrix exponentiation when multiple copies of a quantum state are available.<n>We propose a method to circumvent this limitation by introducing imperfect quantum copies.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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