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 Brisbane, Kyiv, and Sherbrooke. 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.