Quantum Fourier transform (QFT) is an important part of many quantum algorithms. However, there are few reports on fractional (QFRFT). The main reason that the definitions (FRFT) diverse, while some do not include unitarity, which leads to studies pointing out no QFRFT. In this paper, we first present a reformulation weighted (WFRFT) and prove its thereby proposing (QWFRFT). proposal QWFRFT pro...

Abstract Fast (sub-second) spectroscopy with high spectral resolution is of vital importance for revealing quantum chemistry kinetics complex chemical and biological reactions. Fourier transform (FT) spectrometers can achieve operate at hundreds ms time scales in rapid-scan mode. However, the linear translation a scanning mirror imposes stringent time-resolution limitations to these systems, wh...

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and f...