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41st Annual Symposium on Foundations of Computer Science
An improved quantum Fourier transform algorithm and applications
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
L. Hales, S. Hallgren, "An improved quantum Fourier transform algorithm and applications," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 515, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892139, author = {L. Hales and S. Hallgren}, title = {An improved quantum Fourier transform algorithm and applications}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {515}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892139}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  An improved quantum Fourier transform algorithm and applications SN  02725428 SP EP A1  L. Hales, A1  S. Hallgren, PY  2000 KW  Fourier transforms; quantum computing; computational complexity; polynomials; improved quantum Fourier transform algorithm; arbitrary inverse polynomial; Fourier sampling technique; quantum Fourier sampling lemma; arbitrary periodic function; periodic functions; standard quantum lowerbound techniques; maximal class; quantum periodfinding algorithm VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We give an algorithm for approximating the quantum Fourier transform over an arbitrary Z/sub p/ which requires only O(n log n) steps where n=log p to achieve an approximation to within an arbitrary inverse polynomial in n. This improves the method of A.Y. Kitaev (1995) which requires time quadratic in n. This algorithm also leads to a general and efficient Fourier sampling technique which improves upon the quantum Fourier sampling lemma of L. Hales and S. Hallgren (1997). As an application of this technique, we give a quantum algorithm which finds the period of an arbitrary periodic function, i.e. a function which may be manytoone within each period. We show that this algorithm is efficient (polylogarithmic in the period of the function) for a large class of periodic functions. Moreover, using standard quantum lowerbound techniques, we show that this characterization is right. That is, this is the maximal class of periodic functions with an efficient quantum periodfinding algorithm.
Index Terms:
Fourier transforms; quantum computing; computational complexity; polynomials; improved quantum Fourier transform algorithm; arbitrary inverse polynomial; Fourier sampling technique; quantum Fourier sampling lemma; arbitrary periodic function; periodic functions; standard quantum lowerbound techniques; maximal class; quantum periodfinding algorithm
Citation:
L. Hales, S. Hallgren, "An improved quantum Fourier transform algorithm and applications," focs, pp.515, 41st Annual Symposium on Foundations of Computer Science, 2000
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