An Improvement in Quantum Fourier Transform

Abstract

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we introduce a new approach to improve the preciseness of the standard Quantum Fourier Transform. The presented Quantum-SVD algorithm is based on the singular value decomposition mechanism. While the complexity of the proposed scheme is the same as the standard Quantum Fourier Transform, the precision of the Quantum-SVD approach is some orders higher. The Quantum-SVD approach also exploits the benefits of quantum searching.

arXiv comment30 pages, 10 figures, Journal-ref: Journal of Circuits, Systems, and Computers (JCSC), World Scientific, Print ISSN: 0218-1266, Online ISSN: 1793-6454; 2010

References in corpus (7)

• Semiclassical Fourier Transform for Quantum Computation
• Approximate Quantum Fourier Transform and Decoherence
• The Quantum Fourier Transform and Extensions of the Abelian Hidden Subgroup Problem
• Fourier transformation and response functions
• A quantum Fourier transform algorithm
• Optimal Tight Frames and Quantum Measurement
• Quantum Fourier Transform in a Decoherence-Free Subspace

Cited by in corpus (1)

• A Derivative-free Method for Quantum Perceptron Training in Multi-layered Neural Networks