Quantum Computing using Molecular Vibrational and Rotational Modes of the Open-shell $^{14}$N$^{16}$O Molecule

We demonstrate the possibility of using internal molecular vibrational and rotational modes of an open-shell molecule for one of the most important quantum algorithms: the Deutsch-Jozsa algorithm. The molecular system of interest is one of the representative open-shell molecules: $^{14}$N$^{16}$O. The gate pulses are constructed by utilizing multi-target optimal control theory (MTOCT). The gate fidelities of each quantum gate are more than 95.23{\%}. Upon implementing the Deutsch-Jozsa algorithm combining these elementary gates, we obtained fidelity of at least 94.76{\%}. This indicates that vibrational and rotational qubits of the open-shell $^{14}$N$^{16}$O molecule are about as promising for processing quantum algorithms as those of the closed-shell molecule $^{12}$C$^{16}$O that we studied earlier.