International Association
for Cryptologic Research

Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never discussed. In practice, the Xilinx LogiCORE IP Fast Fourier Transform core has the maximum transform size $N=2^{16}$. Taking into account the Planck constant $\hbar=6.62607015\times 10^{-34}$ and the difficulty to physically implement basic operator {\footnotesize $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$} on some qubits, we think $N=2^{120}$ could be an upper bound for the transform size of QFT.