Paper 2023/1971
The Planck Constant and Quantum Fourier Transformation
Abstract
Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never been 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 $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$ on a qubit, we think $N=2^{120}$ could be an upper bound for the transform size of QFT.
Note: In reply to the comments by prof. Mikhail Dyakonov on the early version, we use the formula for energy of a free quantum particle to calculate the upper bound for QFT.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Quantum Fourier Transformationtransform sizedepleted operatorShor algorithmPlanck constant
- Contact author(s)
- caozhj @ shu edu cn
- History
- 2024-03-07: last of 2 revisions
- 2023-12-31: received
- See all versions
- Short URL
- https://ia.cr/2023/1971
- License
-
CC0
BibTeX
@misc{cryptoeprint:2023/1971,
author = {Zhengjun Cao and Zhenfu Cao},
title = {The Planck Constant and Quantum Fourier Transformation},
howpublished = {Cryptology ePrint Archive, Paper 2023/1971},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/1971}},
url = {https://eprint.iacr.org/2023/1971}
}
