Quantum Kravchuk Transform using su(2) fast-forwarding

@misc{guan2026quantum,
  title = {{Quantum Kravchuk Transform using $\mathfraksu(2)$ fast-forwarding}},
  author = {Chaowen Guan and Akshit Katiyar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.08443},
  eprint = {2606.08443},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.08443},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Quantum Kravchuk Transform using su(2) fast-forwarding
AU  - Chaowen Guan
AU  - Akshit Katiyar
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.08443
UR  - https://arxiv.org/abs/2606.08443
AB  - We present a quantum algorithm for the Kravchuk transform that scales logarithmically in both the dimension and the inverse of the error parameter. The quantum Kravchuk transform maps computational basis states to states with amplitudes proportional to Kravchuk functions. We achieve this by combining two key techniques: the structural relationship between the Kravchuk transform and the Lie algebras su(2), and a recent fast-forwarding simulation method for su(2) operators in the oscillator representation. More precisely, we first establish the map from Kravchuk transform in computational basis to su(2) in Fock basis. Then built on this connection, we apply the fast-forwarding to achieve an efficient quantum Kravchuk transform.
ER  -