A Hybrid Quantum-Classical Algorithm for Multichannel Quantum Scattering of Atoms and Molecules

We propose a hybrid quantum-classical algorithm for solvingthetime-independent Schro''dinger equation for atomic and molecularcollisions. The algorithm is based on the S-matrixversion of the Kohn variational principle, which computes the fundamentalscattering S-matrix by inverting the Hamiltonianmatrix expressed in the basis of square-integrable functions. Thecomputational bottleneck of the classical algorithm symmetricmatrix inversion is addressed here using the variational quantumlinear solver (VQLS), a recently developed noisy intermediate-scalequantum (NISQ) algorithm for solving systems of linear equations.We apply our algorithm to single- and multichannel quantum scatteringproblems, obtaining accurate vibrational relaxation probabilitiesin collinear atom-molecule collisions. We also show how thealgorithm could be scaled up to simulate collisions of large polyatomicmolecules. Our results demonstrate that it is possible to calculatescattering cross sections and rates for complex molecular collisionson NISQ quantum processors, opening up the possibility of scalabledigital quantum computation of gas-phase bimolecular collisions andreactions of relevance to astrochemistry and ultracold chemistry.