Mixed Quantum/Classical Theory Approach to Rotationally Inelastic Molecular Collisions Implemented on a Quantum Computer

All elements of a quantum algorithm for calculations of rotationally inelastic molecule + atom scattering within the framework of a mixed quantum/classical theory are outlined. In this approach, the rotational motion of the molecule is described quantum mechanically using the time-dependent Schrödinger equation, while the scattering process of two collision partners is treated classically. The matrix of potential coupling is precomputed on a classical processor, whereas the quantum hardware is used to propagate the system of coupled equations for the rotational state-to-state transitions. All quantum circuits needed for practical implementation of the algorithm are presented. First, the quantum codes written in Qiskit are rigorously tested by running calculations for a N₂ + O collision on a classical emulator of quantum hardware using a realistic potential energy surface of this system and comparing these results against the results obtained by the MQCT code. Next, these codes are run on the actual quantum hardware, such as the publicly available IBM <i>Brisbane</i>, <i>Kyiv,</i> and <i>Sherbrooke</i>. A very good agreement with benchmark data was obtained. To the best of our knowledge, this is the first proof-of-principle calculation of inelastic scattering implemented successfully on a quantum computer using a case study within mixed quantum/classical framework.