Generalized Quantum Fast Transformations via Femtosecond Laser Writing Technique

Quantum computers promise to be able to solve tasks beyond the reach of standard computational platforms. Among the others, photonic quantum walks prove to be great candidates for their implementation, since single photon sources, passive linear optics and photo-detectors are sufficient for universal quantum computation. To this aim, a device performing the quantum Fourier transform represents a fundamental building block for quantum algorithms, whose applications are not limited to the field of quantum computation. Recently, an algorithm has been developed to efficiently realize a quantum Fourier transform of an input photonic state by using a quantum walk on elementary linear-optical components. Here we provide a simple operative description of the algorithm, introducing a whole class of quantum transformations achievable through a generalization of this procedure. We finally discuss how femtosecond laser writing technology well represents an efficient and scalable platform for the implementation of this class of photonic quantum walks.