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Fast parallel circuits for the quantum Fourier transform  (Make Corrections)  (6 citations)
Richard Cleve John Watrous University of Calgary June 1, 2000
IEEE Symposium on Foundations of Computer Science



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Abstract: We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). (Update)

Context of citations to this paper:   More

.... a sequence of standard Hadamard gates and controlled z rotations (the state of the art is summarized and improved by Cleve and Watrous [11]) probably with complexity O(n) or better. Leaving the quantum Fourier transform as a primitive in the byte code will allow each...

...Sampling It is not known how to eciently compute the quantum Fourier transform over Z n exactly. However, ecient approximations are known [6] [10] 11] We can even compute an ecient approximation when n is unknown as long as we have an upper bound on n [10] 2.4 Finite Fields...

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BibTeX entry:   (Update)

@inproceedings{ cleve00fast,
    author = "Richard Cleve and John Watrous",
    title = "Fast parallel circuits for the quantum Fourier transform",
    booktitle = "{IEEE} Symposium on Foundations of Computer Science",
    pages = "526-536",
    year = "2000",
    url = "citeseer.ist.psu.edu/article/cleve00fast.html" }
Citations (may not include all citations):
210   A fast quantum mechanical algorithm for database search - Grover - 1996
206   An algorithm for the machine calculation of complex Fourier .. (context) - Cooley, Tukey - 1965
201   Parallel prefix computation (context) - Ladner, Fischer - 1980
175   Logical reversibility of computation (context) - Bennett - 1973
168   Algorithms for quantum computation: discrete logarithms and .. - Shor - 1994
168   A taxonomy of problems with fast parallel algorithms (context) - Cook - 1985
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124   Elementary gates for quantum computation - Barenco, Bennett et al. - 1995
102   Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997
91   Log depth circuits for division and related problems (context) - Beame, Cook et al. - 1986
88   Approximate formulas for some functions of prime numbers (context) - Rosser, Schoenfeld - 1962
68   Modern Computer Algebra (context) - Gathen, Gerhard - 1999
50   Quantum algorithms revisited - Cleve, Ekert et al. - 1998
43   Probabilistic Proofs and Pseudorandomness (context) - Goldreich - 1999
35   Quantum cryptanalysis of hidden linear functions (context) - Boneh, Lipton - 1995
34   Limits to Parallel Computation (context) - Greenlaw, Hoover et al. - 1995
30   Quantum counting - Brassard, Hyer et al. - 1998
25   Quantum measurements and the abelian stabilizer problem - Yu - 1995
21   Logarithmic depth circuits for algebraic functions (context) - Reif - 1986
21   An approximate Fourier transform useful in quantum factoring (context) - Coppersmith
20   the algorithmic complexity of discrete functions (context) - Ofman - 1963
20   Gauss and the history of the Fast Fourier Transform (context) - Heideman, Johnson et al. - 1984
19   Volume I: Efficient Algorithms (context) - Bach, Shallit et al. - 1996
15   Schnelle multiplikation groer zahlen (context) - Schonhage, Strassen - 1971
13   Generalized FFTs -- a survey of some recent results - Maslen, Rockmore - 1995
12   Parallel quantum computation and quantum codes - Moore, Nilsson - 1998
11   Distinguishability and Accessible Information in Quantum The.. - Fuchs - 1995
10   The re-discovery of the fast Fourier transform algorithm (context) - Cooley - 1987
9   Testing shift-equivalence of polynomials using quantum machi.. - Grigoriev - 1996
9   Quantum Fourier sampling simplified - Hales, Hallgren - 1999
7   Theoria interpolationis methodo nova tractata (context) - Gauss - 1973
7   Quantum searching and counting by eigenvector analysis (context) - Mosca - 1998
6   Quantum Algorithms (context) - Hyer - 2000
5   Polynomial simulations of decohered quantum computers - Aharonov, Ben-Or - 1996
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