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Abstract: Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a generalized Kronecker product is given. Applications include re-development of the networks for computing the Walsh-Hadamard and the quantum Fourier transform. New networks for two wavelet transforms are given. Quantum computation of Fourier transforms for... (Update)
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BibTeX entry: (Update)
@misc{ yer-efficient,
author = "Peter H{\o}yer",
title = "Efficient Quantum Transforms",
url = "citeseer.ist.psu.edu/156805.html" }
Citations (may not include all citations):770 Orthonormal bases of compactly supported wavelets (context) - Daubechies - 1988
210 A fast quantum mechanical algorithm for database search - Grover - 1996
173 Quantum complexity theory - Bernstein, Vazirani - 1997
144 the power of quantum computation - Simon - 1994
135 Computational Frameworks for the Fast Fourier Transform (context) - Van Loan - 1992
126 Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1992
124 Elementary gates for quantum computation - Barenco, Bennett et al. - 1995
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997
73 Tight bounds on quantum searching - Boyer, Brassard et al. - 1996
70 Quantum computational networks (context) - Deutsch - 1989
65 Representation Theory of Finite Groups and Associative Algeb.. (context) - Curtis, Reiner - 1962
52 Good quantum error-correcting codes exist - Calderbank, Shor - 1996
45 Quantum computation - Berthiaume - 1997
45 Polynomial-time algorithms for prime factorization and discr.. (context) - Shor - 1997
42 Multiple particle interference and quantum error correction (context) - Steane - 1996
42 The quantum challenge to structural complexity theory - Berthiaume, Brassard - 1994
37 Quantum error correction and orthogonal geometry (context) - Calderbank, Rains et al. - 1997
34 Class of quantum error-correcting codes saturating the quant.. (context) - Gottesman - 1996
28 Scheme for reducing decoherence in quantum computer memory (context) - Shor - 1995
25 Quantum measurements and the Abelian stabilizer problem - Yu - 1995
20 Quantum computation of Fourier transforms over symmetric gro.. (context) - Beals - 1997
16 Quantum networks for elementary arithmetic operations (context) - Vedral, Barenco et al. - 1996
15 Simple quantum error-correcting codes (context) - Steane - 1996
15 Semiclassical Fourier transform for quantum computation - Griffiths, Niu - 1996
13 Generalized FFTs---A survey of some recent results - Maslen, Rockmore - 1995
7 unitary matrices and signal processing applications (context) - Regalia, Mitra - 1989
7 Quantum cryptoanalysis of hidden linear functions (context) - Boneh, Lipton - 1995
4 ard. R'esolution d'une question relative aux d'eterminants (context) - Hadam
3 Linear Representations of Finite Groups (context) - Serre - 1977
3 A note on computing Fourier transformation by quantum progra.. (context) - Cleve - 1994
2 Quantum circuit complexity - Yao - 1993
1 Testing the shift-equivalence of polynomials using quantum m.. (context) - Yu - 1996
1 A closed set of normal orthogonal functions (context) - Leonard - 1923
1 Zur theorie der orthogonalen funktionensysteme (context) - Haar - 1910
1 A unified treatment of discrete fast unitary transforms (context) - Fino, Algazi - 1977
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A Quantum Algorithm for Finding the Minimum - Dürr, Høyer (1996) (Correct)
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