# The amplified quantum Fourier transform: solving the local period problem

The amplified quantum Fourier transform: solving the local period problem This paper creates and analyzes a new quantum algorithm called the Amplified Quantum Fourier Transform (QFT) for solving the following problem: The Local Period 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 $$A=\{j:j=s+rP,r=0,1\ldots M-1\}$$ where $${P\leq \sqrt{N}}$$ and $${M \ll N}$$ , and where M is assumed known. Given an oracle f : L→ {0,1} which is 1 on A and 0 elsewhere, find the local period P and the offset s. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# The amplified quantum Fourier transform: solving the local period problem

Quantum Information Processing, Volume 12 (2) – Aug 15, 2012
29 pages

/lp/springer_journal/the-amplified-quantum-fourier-transform-solving-the-local-period-7tI6wRrwXV
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-012-0468-6
Publisher site
See Article on Publisher Site

### Abstract

This paper creates and analyzes a new quantum algorithm called the Amplified Quantum Fourier Transform (QFT) for solving the following problem: The Local Period 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 $$A=\{j:j=s+rP,r=0,1\ldots M-1\}$$ where $${P\leq \sqrt{N}}$$ and $${M \ll N}$$ , and where M is assumed known. Given an oracle f : L→ {0,1} which is 1 on A and 0 elsewhere, find the local period P and the offset s.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 15, 2012

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