Fast quantum Fourier-Weyl-Heisenberg transforms / Labunets V.G., Rundblad-Labunets E.V., Astola J. // Proceedings of SPIE - The International Society for Optical Engineering. - 2001. - V. 4386, l. . - P. 121-132.

ISSN:
0277786X
Type:
Conference Paper
Abstract:
The quantum fourier transforms on Abelian groups was identified as a powerful tool for developing quantum algorithms. Fast fourier transforms (FFT) on finite albelian groups were widely used in signal processing. In classical signal processing a new classes of unitary transforms was started for possible applications. The harmonic analysis of functions on discrete one dimesional and n dimensional Heisenberg-wely groups and the Galois fields were also studied.
Author keywords:
Fast algorithms; Fourier transforms; Non-commutative groups; Quantum computer
Index keywords:
Algorithms; Computational methods; Fast Fourier transforms; Hamiltonians; Inverse problems; Linear algebra; Quantum theory; Weyl-Heisenberg transforms; Signal processing
DOI:
10.1117/12.434210
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-0034779191&doi=10.1117%2f12.434210&partnerID=40&md5=ca324e13823aff77c7dc9133a41ffbe7
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-0034779191&doi=10.1117%2f12.434210&partnerID=40&md5=ca324e13823aff77c7dc9133a41ffbe7
Affiliations Dept. of Automat. and Info. Technol., Urals State Technical University, Ekaterinburg, Russian Federation
Author Keywords Fast algorithms; Fourier transforms; Non-commutative groups; Quantum computer
References Labunets, V.G., Quaternion number-theoretical transform (1981) Devices and Methods of Experimental Investigations in Automation (in Russian), pp. 28-33. , Dnepropetrovsk State University Pressw, Dnepropetrovsk; Labunets, V.G., Fast Fourier transform for Generalized Dihedral groups (1985) Design Automatization Theory and Methods (in Russian), pp. 135-142. , Institute Technical Cybernetics: BSSR SA Press, Minsk; Labunets, E.V., Labunets, V.G., Creutzburg, R., Construction and complexity of a new FFT algorithms over commutative ring with identity for dihedral and quaternion groups (1996) Recent Developments in Abstract Harmonic Analysis with Applications in Signal Processing, pp. 445-464. , Nauka, Belgrade; Aizenberg, N.N., Semirot, M.S., Computer signal processing on finite groups (1983) Orthogonal Methods Application in Signal Processing and System Analysis (in Russian), pp. 53-73. , Ural Politechnical Institute Press, Sverdlovsk; Labunets, V.G., Fast Fourier transform for affine groups Aff(GF(p)) over Galois fields (1984) Device and Methods of Experimental Investigations Automatization (in Russian), pp. 60-65. , Dnepropetrovsk State University Press, Dnepropetrovsk; Berman, S., Grushko, I., Theory of discrete signal processing (1984) Probl. Inf. Transm., 19, p. 284; Labunets, E.V., Labounets, V.G., Creutzburg, R., Construction and complexity of a new FFT algorithms over commutative ring with identity for metacyclic groups (1996) Recent Developments in Abstract Harmonic Analysis with Applications in Signal Processing, pp. 421-443. , Nauka, Belgrade; Clausen, M., FFT for Metabelian Groups (1989) SIAM J. Comp, 18, pp. 584-593; Baum, U., Claussen, M., Tietz, B., (1990) Improved upper complexity bounds for the discrete Fourier transform, p. 25. , Preprint, University of Bonn, January; Labunets-Rundblad, E.V., Labunets, V.G., Fast Fourier-Weyl Transform (2000) Signal Processing X, Theories and Applications, pp. 505-508. , Eusipco-2000, Tampere, Finland, 4-8 September; Labunets-Rundblad, E.V., Labunets, V.G., Fast Fourier-Weyl-Heisenberg Transforms (2000) Signal Processing X, Theories and Applications, pp. 2353-2356. , Eusipco-2000, Tampere, Finland, 4-8 September; Labunets-Rundblad, E.V., Labunets, V.G., Astola, J., Egiazarian, K., Fast Fourier-Heisenberg Transforms (2000) IEEE Inter. Conf. on ASSP, pp. 540-543. , June 5-9, Istanbul, Turkey; Stancovic, R.S., Morago, C., Astola, J., (1999) Readings in Fourier Analysis on Finite non-Abelian groups, 5. , TICSP Series, TUT, Tampere; Beth, Th., (1984) Verfahren der Schellen Fourier Transformation, , Teubner, Stuttgart; Clausen, M., Baum, U., (1993) Fast Fourier Transforms, , Wissenschaftsverlag, Manheim; Maslen, D., Rockmore, D., Generalized FFT's - A survey of some recent results (1996) DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Groups and Computation, 2, pp. 183-237. , L. Finkelstein and W. Kantor (eds); Curtis, C., Reiner, I., (1962) Representation Theory of Finite Groups and Associative Algebras, , Wiley, New York; Kitaev, A.Yu., (1997) Quantum measurement and the Abelian Stabilizer problem, , LANL preprint quant-ph/9702028, Feb; Vedral, V.V., Barenco, A., Ekert, A., Quantum networks for elememtary arithmetic operations Physical Review A, 54, pp. 147-153; Hoyer, P., (1997) Efficient quantum transforms, , LANL preprint quant-ph/9702028, Feb; Fijany, A., Williams, C.P., (1998) Quantum wavelet transforms: Fast algorithms and complete circuits, , LANL preprint quant-ph/9800904, Sep; Labunets, V.G., (1984) Algebraic Theory of Signals and Systems. P.1 (in Russian), , Krasnoyarsk State University Press, Krasnoyarsk; Labunets, V.G., Labunets-Rundblad, E.V., Astola, J., Introduction to quantum and hyperquantum information tecnologies. P.1: Real probability and unreal probabilities (2000) Proc. of First International Workshop on Spectral Tecniques and Logic Design for Future Digital Systems, pp. 283-321. , Tampere, Finland, June 2-3
Correspondence Address Labunets, V.G.; Dept. of Automat. and Info. Technol., Urals State Technical University, Ekaterinburg, Russian Federation; email: lab@cs.tut.fi
Editors Donkor E.Pirich A.R.Taylor E.W.
Sponsors SPIE
Conference name Photonic and Quantum Technologies for Aerospace Applications III
Conference date 17 April 2001 through 18 April 2001
Conference location Orlando,FL
Conference code 58665
CODEN PSISD
Language of Original Document English
Abbreviated Source Title Proc SPIE Int Soc Opt Eng
Source Scopus