Entanglement of periodic states, the quantum fourier transform, and shor's factoring algorithm

Yonatan Most*, Yishai Shimoni, Ofer Biham

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely on the quantum Fourier transform. Since entanglement is believed to be a necessary resource for quantum computational speedup, we analyze the entanglement of periodic states and the way it is affected by the quantum Fourier transform. To this end, we derive a formula that evaluates the Groverian entanglement measure for periodic states. Using this formula, we explain the surprising result that the Groverian entanglement of the periodic states built up during the preprocessing stage is only slightly affected by the quantum Fourier transform.

Original languageAmerican English
Article number052306
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume81
Issue number5
DOIs
StatePublished - 7 May 2010

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