Quantum Pseudo-Fractional Fourier Transform Using Multiple-Valued Logic

This paper presents the multivalued logic version of the quantum pseudo-fractional Fourier transform (QFrFT), which is a more general transform of which the widely used quantum Fourier transform (QFT) is a special case. We also show how to efficiently implement the QPFrFT using O(n³) two qudit rotation gates. It is possible to implement an approximate QPFrFT by eliminating the rotation gates which implement exponentially decreasing rotation angles. The multivalued logic QPFrFT has improved approximation properties as the radix d of the logic used increases. The binary QPFrFT has the same circuit complexity and yet has the worst approximation properties when compared to multivalued logic implementations.