The Amplified Quantum Fourier Transform (Amplified-QFT)

Details The Amplified Quantum Fourier Transform (Amplified-QFT) The Amplified Quantum Fourier Transform (Amplified-QFT)

2010-09-30

arxiv.org/abs/1010.0033v1

Physics

Quantum Physics

21 pages

Scientific paper

In this paper we show how to use Grover's algorithm to amplify and enhance the period finding capability of the quantum Fourier Transform (QFT). In particular we create a quantum algorithm called the Amplified-QFT algorithm which solves the following problem: The Local Period Finding Problem: Let L={0,1,...,N-1} be a set of N labels, and let A be a subset of M labels of period P, i.e. a subset of the form A={j: j=s+rP,r=0,1,...,M-1} where P{0,1} which is 1 on A and 0 elsewhere, find the period P. The Amplified-QFT algorithm which solves this problem consists of 3 steps. Step 1: Apply Grover's algorithm without measurement to amplify the amplitudes of the M labels of the set A. Step 2: Apply the QFT to the resultant state. Step 3: Measurement. We examine the probabilities of success of three algorithms a) the Amplified-QFT 2) the QFT and 3) the QHS algorithms. We also show how to recover the offset s.

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