R. Cleve. A note on computing quantum Fourier transforms by quantum programs. Manuscript. Available at http://www.cpsc.ucalgary.ca/ cleve/papers.html, 1994. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Fast parallel circuits for the quantum Fourier transform - Richard Cleve John Self-citation (Cleve) (Correct)
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R. Cleve. A note on computing quantum Fourier transforms by quantum programs. Manuscript. Available at http://www.cpsc.ucalgary.ca/ cleve/papers.html, 1994.
Fast parallel circuits for the quantum Fourier transform - Richard Cleve John Self-citation (Cleve) (Correct)
No context found.
R. Cleve. A note on computing quantum Fourier transforms by quantum programs. Manuscript. Available at http://www.cpsc.ucalgary.ca/~cleve/papers.html, 1994.
Fast parallel circuits for the quantum Fourier transform - Cleve, Watrous (2000) (6 citations) Self-citation (Cleve) (Correct)
.... The fact that the QFT can be performed by quantum circuit with size polynomial in log m for some values of m was first observed by Shor [33] In the case where m = 2 n , there exist quantum circuits performing the QFT with O(n 2 ) gates, which was proved by Coppersmith [13] see also [10]) These circuits are based on a recursive description of the QFT that is analogous to the description of the DFT exploited by the FFT. While in some sense these quantum circuits are exponentially faster than the classical FFT, the task that they perform is quite different. The QFT does not ....
....is possible to compute the QFT exactly with a near linear number of gates. Theorem 4 For every n there exists a quantum circuit that exactly computes the QFT modulo 2 n that has size O(n(log n) 2 log log n) and depth O(n) Theorem 4 is based on a nonstandard recursive description of the QFT [10] combined with an asymptotically fast multiplication algorithm [32] While it is sufficient to use the QFT with respect to power of 2 moduli in Shor s algorithm, one may wish to perform the QFT with respect to other moduli when considering other problems. By exploiting a relationship among QFTs ....
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R. Cleve. A note on computing quantum Fourier transforms by quantum programs. Manuscript. Available at http://www.cpsc.ucalgary.ca/ cleve/papers.html, 1994.
Fast parallel circuits for the quantum Fourier transform - Cleve, Watrous (2000) (6 citations) Self-citation (Cleve) (Correct)
....Shor s original method may be described as a mixed radix method, and is discussed further in Section 7.2. In the particular case where m = 2 n , there exist quantum circuits performing the quantum Fourier transform with O(n 2 ) gates, which was proved by Coppersmith [14] see also [9]) These circuits are based on a recursive description of the QFT that is analogous to the description of the DFT exploited by the FFT. While in some sense these quantum circuits are exponentially faster than the classical FFT, the task that they perform is quite different. The QFT does not ....
....it is possible to compute the QFT exactly with a near linear number of gates. Theorem 2 For any n there is a quantum circuit that exactly computes the QFT modulo 2 n that has size O(n(log n) 2 log log n) and depth O(n) Theorem 2 is based on a nonstandard recursive description of the QFT [9] combined with an asymptotically fast multiplication algorithm [33] There are several reasons why we believe results regarding quantum circuit complexity, such as in the above theorems, are important. First, circuit depth is likely to be particularly relevant in the quantum setting for physical ....
R. Cleve. A note on computing quantum Fourier transforms by quantum programs. Manuscript. Available at http://www.cpsc.ucalgary.ca/~cleve/papers.html, 1994.
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