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It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis and compression in diagnostics, astronomy, chemistry and broadcasting builds on the discrete Fourier transform. It is implemented with the Fast Fourier Transform (FFT) algorithm that assumes a periodic input of specific lengths, which rarely holds true. A less-known transform, the Kravchuk-Fourier (KT), allows one to operate on finite strings of arbitrary length. It is of high demand in digital image processing and computer vision, but features a prohibitive runtime. Here, we report a one-step computation of a fractional quantum KT. A quantum $d$-nary (qudit) architecture we use comprises only one gate and offers processing time independent of the input size. The gate may employ a multiphoton Hong-Ou-Mandel effect. Existing quantum technologies may scale it up towards diverse applications.
By popular request we post these old (from 2001) lecture notes of the Varenna Summer School Proceedings. The original was published as J. I. Cirac, L. M. Duan, and P. Zoller, in Experimental Quantum Computation and Information Proceedings of the Inte
As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developi
Quantum computing is an attractive and multidisciplinary field, which became a focus for experimental and theoretical research during last decade. Among other systems, like ions in traps or superconducting circuits, solid-states based qubits are cons
Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular appeal, since
Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of ch