Quantum hashing algorithm implementation

We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. This algorithm is based on a quantum finite automaton for a unary language $\mathtt{MOD_p}$, where $ \mathtt{MOD_p} = \{ a^{i \cdot p} \mid i \geq 0 \} $, for any prime number $p$. We consider 16-qubit and 27-qubit IBMQ computers with the special graphs of qubits representing nearest neighbor architecture that is not Linear Nearest Neighbor (LNN) one. We optimize quantum circuits for the quantum hashing algorithm with respect to minimizing the number of control operators as the most expensive ones. We apply the same approach for an optimized circuit implementation of Quantum Fourier Transform (QFT) operation on the aforementioned machines because QFT and hashing circuits have common parts.