TY - JOUR

T1 - Entanglement of periodic states, the quantum fourier transform, and shor's factoring algorithm

AU - Most, Yonatan

AU - Shimoni, Yishai

AU - Biham, Ofer

PY - 2010/5/7

Y1 - 2010/5/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77952374232&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.81.052306

DO - 10.1103/PhysRevA.81.052306

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AN - SCOPUS:77952374232

SN - 1050-2947

VL - 81

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 5

M1 - 052306

ER -