In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today’s computers, our proposed device performs DFTs at the frequency of the computer clock speed.

1.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, New York, 2000).
2.
D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
3.
S. Braunstein and H.-K. Lo, Scalable Quantum Computers: Paving the Way to Realization (Wiley, New York, 2001).
4.
C. Williams and S. Clearwater, Explorations in Quantum Computing (Telos, Santa Clara, 1998).
5.
G. Berman, G. Doolen, R. Mainieri, and V. Tsifrinovitch, Introduction to Quantum Computers (World Scientific, Singapore, 1998).
6.
H.-K. Lo, S. Popescu, and T. Spiller, Introduction to Quantum Computation and Information (World Scientific, Singapore, 1998).
7.
P. Shor, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alomitos, 1994), p. 124.
8.
L. K.
Grover
,
Phys. Rev. Lett.
79
,
325
(
1997
).
9.
L. K.
Grover
,
Phys. Rev. Lett.
79
,
4709
(
1997
).
10.
J.
Ahn
,
T. C.
Weinacht
, and
P. H.
Bucksbaum
,
Science
287
,
463
(
2000
).
11.
M. N.
Leuenberger
and
D.
Loss
,
Nature (London)
410
,
789
(
2001
).
12.
M. N.
Leuenberger
,
D.
Loss
,
M.
Poggio
, and
D. D.
Awschalom
,
Phys. Rev. Lett.
89
,
207601
(
2002
);
M. N.
Leuenberger
and
D.
Loss
,
Phys. Rev. B
68
,
165317
(
2003
).
13.
M. Gu, T. Asakura, K. H. Brenner, T. W. Hansch, F. Krausz, W. T. Rhodes, and H. Weber, Advanced Optical Imaging Theory (Springer, New York, 1999).
14.
J. W. Goodman, Introduction to Fourier Optics 2nd Ed. (McGraw-Hill, New York, 1996).
15.
J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
16.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd Ed. (Cambridge University, New York, 1999).
17.
J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading MA, 1994).
18.
J. D. Jackson, Classical Electrodynamics, 2nd Ed. (Wiley, New York, 1975), Sec. 10.
19.
J. M.
Kikkawa
and
D. D.
Awschalom
,
Science
287
,
473
(
2000
).
20.
W.
Becker
,
A.
Bergmann
,
K.
Koenig
, and
U.
Tirlapur
,
Proc. SPIE
4262
,
414
(
2001
).
21.
D. D. Awschalom, D. Loss, and N. Samarth, Semiconductor Spintronics and Quantum Computation (Springer, New York, 2002).
22.
S. A.
Wolf
,
D. D.
Awschalom
,
R. A.
Buhrman
,
J. M.
Daughton
,
S.
von Molnar
,
M. L.
Roukes
,
A. Y.
Chtchelkanova
, and
D. M.
Treger
,
Science
294
,
1488
(
2001
).
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