In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier...

In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent...

fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...

Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...

algebraic problems. The quantum Fourier transform is the quantum analogue of the discrete Fourier transform, and is used in several quantum algorithms. The Hadamard...

Fourier-related transforms Laplace transform (LT) Two-sided Laplace transform Mellin transform Non-uniform discrete Fourier transform (NDFT) Quantum Fourier transform...

Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts...

the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

transform Fourier amplitude sensitivity testing Fourier optics Quantum mechanics, for Wavefunctions Uncertainty principle Quantum Fourier transform Periodic...

Time–frequency representation Quantum Fourier transform Topological abelian group Haar measure Discrete Fourier transform Dirichlet character Amenable...

implementing f {\displaystyle f} as a quantum transform, followed finally by a quantum Fourier transform. Due to this, the quantum algorithm for computing the discrete...

on the state. Quantum Fourier transform is the quantum analogue of the classical discrete Fourier transform (DFT), as it takes quantum states represented...

manual: Quantum Memory Management Ryo, Asaka; Kazumitsu, Sakai; Ryoko, Yahagi (2020). "Quantum circuit for the fast Fourier transform". Quantum Information...

The final part of the circuit involves applying the inverse quantum Fourier transform (QFT) Q F T {\displaystyle {\mathcal {QFT}}} on the first register...

In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which...

irreducible representations of larger dimension for abelian groups. The quantum fourier transform can be defined in terms of Z N {\displaystyle \mathrm {Z} _{N}}...

; Wineland, D.J. (2005). "Implementation of the semiclassical quantum Fourier transform in a scalable system". Science. 308 (5724): 997–1000. Bibcode:2005Sci...

Engin (2020). "Quantum arithmetic operations based on quantum Fourier transform on signed integers". International Journal of Quantum Information. 18...

finite groups. These algorithms depend on the primitive of the quantum Fourier transform. No mathematical proof has been found that shows that an equally...

quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn generalizes the Fourier transform. Roughly...

exponentiation with binary constants (all modulus n) The quantum fourier transform Data types Quantum - qureg, quvoid, quconst, quscratch, qucond Classical...

finite-dimensional space (the celebrated discrete Fourier transform being a prime example), one might expect that some quantum circuit could be designed to carry out...

The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 1998, who was then at the University of New South Wales...

stand for: Quantum field theory, the theory of quantum mechanics applied to fields Quantum Fourier transform, a Fourier transform acting on quantum bits Quadratic...

Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier inversion theorem Fourier sine and cosine series Fourier transform Gibbs...

0 ) {\displaystyle {\hat {\psi }}(k,0)} , which is the Fourier transform of the initial quantum state ψ ( x , 0 ) {\displaystyle \psi (x,0)} . It is not...

follow the quantum phase estimation algorithm scheme: we apply controlled Grover operations followed by inverse quantum Fourier transform; and according...

Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms...

Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and...