منابع مشابه
Exact quantum Fourier transforms and discrete logarithm algorithms
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order 2n is needed, and this can be done exactly. Kitaev [9] showed how to approximate the Fourier transform for any order. Here we show how his construction can be made exact by using the technique known as “amp...
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Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importanc...
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Fractional Fourier transforms (FrFT) are a natural one-parameter family of unitary transforms that have the ordinary Fourier transform embedded as a special case. In this paper, following the efforts of several authors, we explore the theory and applications of FrFT, from the standpoints of both quantum mechanics and analysis. These include the phase plane interpretation of FrFT, FrFT’s role in...
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The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1, 1) group. A weight on the C *-algebra of continuous functions vanishing at infinity on the quantum SU(1, 1) group is studied, which is left and right invariant in a weak sense with respect to a product defined using Wall functions. The Haar weight restricted to certain subalgebras a...
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Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant ...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2006
ISSN: 1549-6325,1549-6333
DOI: 10.1145/1198513.1198525