Quantum fast Fourier transform and quantum computation by linear optics
Ronen Eliezer Barak, Y. Ben-Aryeh · Journal of the Optical Society of America B · 2007
Using the quantum fast Fourier transform in linear optics the input mode annihilation operators {â0,â1,...,âs−1} are transformed into output mode annihilation operators {b̂0,b̂1,...,b̂s−1}. We show how to implement experimentally such transformations based on the Cooley-Tukey algorithm, by the use of beam splitters and phase shifters in a linear optical system. Optical systems implementing 1,2, and 3 qubits discrete Fourier transform (DFT) are described, and a general method for implementing the n-qubit DFT is analyzed. These transformations are used on various input radiation states by which phase estimation and order finding can be computed.