Quantum fast Fourier transform and quantum computation by linear optics

摘要

Using the quantum fast Fourier transform in linear optics the input mode annihilation operators {(a) over cap (0), (a) over cap (1),..., (a) over cap (s-1)} are transformed into output mode annihilation operators {(b) over cap (0), (b) over cap (1),... (b) over cap (s-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. (c) 2007 Optical Society of America.