R. Cleve and J. Watrous, \Fast parallel circuits for the quantum Fourier transform," Proceedings of the 41st Annual Symposium on Foundations of Computer Science (2000), 526-536. Home/Search Document Details and Download
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Quantum Algorithms for some Hidden Shift Problems - van Dam, Hallgren, Ip (2003) (1 citation) (Correct)
....2 th root of unity for su#ciently large n. Use a second query to f to reversibly uncompute the f(x) from the second register. 2.3 Approximate Fourier Sampling It is not known how to e#ciently compute the quantum Fourier transform over Z nZ exactly. However, e#cient approximations are known [26, 27, 11, 21]. We can even compute an e#cient approximation to the distribution induced when n is unknown as long as we have an upper bound on n [21] We will need to approximately Fourier sample to solve the unknown n case of the shifted character problem in Section 5.2. To Fourier sample a state ##, we ....
Richard Cleve and John Watrous. Fast parallel circuits for the quantum Fourier transform. Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 526--536, 2000.
Quantum Algorithms for Hidden Coset Problems - van Dam, Hallgren, Ip (2001) (2 citations) (Correct)
....approximated arbitrarily closely by approximating the phase of f(x) to the nearest 2 n th root of unity for suciently large n. 3 2.3 Approximate Fourier 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 The elements of a nite eld F q (where q = p r for some prime p) can be represented as polynomials in F p [X] modulo a degree r irreducible polynomial in F ....
Richard Cleve and John Watrous. Fast parallel circuits for the quantum Fourier transform. In Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 526-536, 2000.
Toward an Architecture for Quantum Programming - Bettelli, Calarco, Serafini (2001) (6 citations) (Correct)
.... P z ( 1) x z j z i where x z is the bitwise scalar product of x and z (the parity of x with respect to z) 12 the transform at low level more eciently than 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 particular architecture to perform hardware optimizations. 2.4 Assumptions on quantum hardware The real computational complexity of a quantum algorithm depends on ....
Richard Cleve, John Watrous, \Fast parallel circuits for the quantum Fourier transform ", Proceedings (FOCS '00), 41st Annual IEEE Symposium on Foundations of Computer Science (2000) pp.526-536, quant-ph/0006004
Parallel Quantum Computation and Quantum Codes - Moore, Nilsson (1998) (9 citations) (Correct)
....2n 1 layers. Can it be parallelized to less than linear depth O(n 2 ) gates [6, 21] Careful inspection shows that the QFT can in fact be parallelized to O(n) depth as shown in Figure 19 (an upside down version of which appears in [12] but it seems dicult to do any better. Cleve and Watrous [5] have shown that fast parallel circuits exist for an approximate QFT, with error small enough to implement Shor s factoring algorithm; this shows that factoring is in ZPP BQNC , and leaves iterated exponentiation as the main bottleneck. They also showed that any constant error circuit must have ....
R. Cleve and J. Watrous, \Fast parallel circuits for the quantum Fourier transform. " Proc. 41st Symp. on Foundations of Computer Science (2000).
Quantum Lower Bounds for Fanout - Fang, Fenner, Green, Homer, Zhang (2003) (Correct)
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R. Cleve and J. Watrous, \Fast parallel circuits for the quantum Fourier transform," Proceedings of the 41st Annual Symposium on Foundations of Computer Science (2000), 526-536.
Quantum Lower Bounds for Fanout - Fang, al. (2003) (Correct)
No context found.
R. Cleve and J. Watrous, \Fast parallel circuits for the quantum Fourier transform," Proceedings of the 41st Annual Symposium on Foundations of Computer Science (2000), 526-536.
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