Quantum algorithms and the Fourier transform
نویسندگان
چکیده
منابع مشابه
Quantum Algorithms and the Fourier Transform
The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a unified way of understanding the efficacy of the algorithms. Finally we describe an efficient quantum factoring algorithm based on a general formalism of Kitaev a...
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The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P (·), both of which are 2× 2 unitary matrices as operators on the two-dimensional 1-qubit space. In this paper, we show thatH and P (·) suffice to generate the unitary group U(2) and, consequently, through controlled-U operations...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 1998
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.1998.0163