Quantifying computational advantage of Grover´s algorithm with the trace speed

Year: 2021

Authors: Gebhart V.; Pezzè L.; Smerzi A.

Autors Affiliation: QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, Firenze, 50125, Italy; Università degli Studi di Napoli Federico II, Via Cinthia 21, Napoli, 80126, Italy

Abstract: Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover?s search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.


Volume: 11 (1)      Pages from: 1288-1  to: 1288-7

More Information: The authors acknowledge financial support from the European Union´s Horizon 2020 research and innovation programme-Qombs Project, FET Flagship on Quantum Technologies Grant no. 820419.
KeyWords: quantum algorithms
DOI: 10.1038/s41598-020-80153-z