[Resource Topic] 2023/1971: The Planck Constant and Quantum Fourier Transformation

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The Planck Constant and Quantum Fourier Transformation

Authors: Zhengjun Cao, Zhenfu Cao


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.

ePrint: https://eprint.iacr.org/2023/1971

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