  We simulate the evolution of three-node spin chain on the quantum processor
of IBM Quantum Experience using the diagonalization of $XX$-Hamiltonian and
representing the evolution operator in terms of CNOT operations and one-qubit
rotations. We study the single excitation transfer from the first to the third
node and show the significant difference between calculated and theoretical
values of state transfer probability. Then we propose a method reducing this
difference by applying the two-parameter transformation including the shift and
scale of the calculated probabilities. { We demonstrate the universality of
this transformation inside of the class of three-node evolutionary systems
governed by the $XX$-Hamiltonian.

Quantum Physics