The special case of cyclotomic fields in quantum algorithms for unit groups

ePrint Report: The special case of cyclotomic fields in quantum algorithms for unit groups

Razvan Barbulescu, Adrien Poulalion

Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is $\tilde{O}(m^5)$. In this work we propose a modification of the algorithm for which the number of qubits is $\tilde{O}(m^2)$ in the case of cyclotomic fields. Moreover, under a recent conjecture on the size of the class group of $\mathbb{Q}(\zeta_m+\zeta_m^{-1})$, the …

algorithm algorithms case eprint report fast modification quantum quantum algorithms qubits report special under work