Quantifying computational advantage of Grover´s algorithm with the trace speed
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.
Journal/Review: SCIENTIFIC REPORTS
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 algorithmsDOI: 10.1038/s41598-020-80153-z