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2021
Let us recall the main definitions associated with the classical Fourier transform known from the course of mathematical analysis. The Fourier transform is one of the central methods of modern applied mathematics [1, 2]. Consider a function \(s:\mathbb {R}\rightarrow \mathbb {C}\). Let s(t) be absolutely integrable on its domain of definition, that is \
Sergei Kurgalin, Sergei Borzunov
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Let us recall the main definitions associated with the classical Fourier transform known from the course of mathematical analysis. The Fourier transform is one of the central methods of modern applied mathematics [1, 2]. Consider a function \(s:\mathbb {R}\rightarrow \mathbb {C}\). Let s(t) be absolutely integrable on its domain of definition, that is \
Sergei Kurgalin, Sergei Borzunov
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2021
Quantum Fourier transform (QFT) plays a key role in many quantum algorithms, but the existing circuits of QFT are incomplete and lacking the proof of correctness. Furthermore, it is difficult to apply QFT to the concrete field of information processing.
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Quantum Fourier transform (QFT) plays a key role in many quantum algorithms, but the existing circuits of QFT are incomplete and lacking the proof of correctness. Furthermore, it is difficult to apply QFT to the concrete field of information processing.
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Quantum Fractional Fourier Transform
Frontiers in Optics / Laser Science, 2018Fourier transform has taken place in different areas and applications, in this paper has been revised an important new form of application in the paradigm of quantum computing. Quantum Fourier transforms have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology [2]. In the Shor’s Algorithm it is used for find
Yesid Madrid +2 more
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Simulating the Quantum Fourier Transform
2013 2nd Workshop-School on Theoretical Computer Science, 2013Quantum Computing is a computational paradigm that takes into account the laws of Quantum Physics in the steps of the computation which advantages were verified both in Computation and Communications. No scalable quantum computer was developed so far and to execute, to test, and to create new quantum algorithms the simulation of quantum computers on ...
Francisco Revson Fernandes Pereira +2 more
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2009
The FT has many applications, particularly in the fields of quantum computation and quantum information. In these fields, the FT is often called the quantum Fourier transform. Traditionally, notation used in quantum physics (i.e., the Dirac notation) to denote vectors is different from that used in mathematics.
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The FT has many applications, particularly in the fields of quantum computation and quantum information. In these fields, the FT is often called the quantum Fourier transform. Traditionally, notation used in quantum physics (i.e., the Dirac notation) to denote vectors is different from that used in mathematics.
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Fourier Transforms and Quantum Computation
2002The foundations of computer science are built upon the modified Church-Turing thesis. This thesis states that any reasonable model of computation can be simulated by a probabilistic Turing Machine with at most polynomial factor simulation overhead (see [10] for a discussion). Early interest in quantum computation from a computer science perspective was
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