Abstract

Using the quantum fast Fourier transform in linear optics the input mode annihilation operators $\{{\widehat{a}}_0,{\widehat{a}}_1,\dots ,{\widehat{a}}_{s-1}\}$ are transformed into output mode annihilation operators $\{{\widehat{b}}_0,{\widehat{b}}_1,\dots ,{\widehat{b}}_{s-1}\}$. 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.

© 2007 Optical Society of America

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