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The quantum Fourier transform is the classical discrete Fourier transform applied to the vector of amplitudes of a quantum state, which has length if it is applied to a register of qubits. The classical Fourier transform acts on a vector and maps it to the vector according to the formula: where is an N -th root of unity.
Thus, this quantum-mechanical bound precludes a Wigner function which is a perfectly localized δ-function in phase space, as a reflection of the uncertainty principle. [6] 10. The Wigner transformation is simply the Fourier transform of the antidiagonals of the density matrix, when that matrix is expressed in a position basis. [7]
The quantum Fourier transform is the quantum analogue of the discrete Fourier transform, and is used in several quantum algorithms. The Hadamard transform is also an example of a quantum Fourier transform over an n-dimensional vector space over the field F 2. The quantum Fourier transform can be efficiently implemented on a quantum computer ...
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared ...
In the case of NMR spectra, the process is relatively straight forward, because the line shapes are Lorentzian, and the convolution of a Lorentzian with another Lorentzian is also Lorentzian. The Fourier transform of a Lorentzian is an exponential. In the co-domain (time) of the spectroscopic domain (frequency) convolution becomes multiplication.
In the generalized version of the Bloch theorem, the Fourier transform, i.e. the wave function expansion, gets generalized from a discrete Fourier transform which is applicable only for cyclic groups, and therefore translations, into a character expansion of the wave function where the characters are given from the specific finite point group.
t. e. In quantum field theory, the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula is a method to calculate S -matrix elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory. It is a step of the path that starts from the Lagrangian of some quantum field theory and leads to prediction of ...
In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex -valued function of frequency.