a hybrid quantum algorithm for time-independent quantum scattering problems

We propose a hybrid quantum-classical algorithm for solving molecular quantum scattering problems, which are central to atmospheric chemistry, combustion, and astrochemistry. The algorithm is based on the S-matrix version of the Kohn variational principle proposed by Zhang, Chu, and Miller [J. Chem. Phys. 88, 6233 (1988)], in which the quantum scattering problem is mapped onto a symmetric matrix inversion problem. The latter is solved on a noisy intermediate-scale quantum processor using the variational quantum linear solver (VQLS) algorithm [Bravo-Prieto et al, arXiv:1909.05820]. Applications to one and two-dimensional scattering problems are presented to validate the approach.