  We propose a hybrid quantum-classical framework to solve the elastic
scattering phase shift of two well-bound nuclei in an uncoupled channel. Within
this framework, we develop a many-body formalism in which the continuum
scattering states of the two colliding nuclei are regulated by a weak external
harmonic oscillator potential with varying strength. Based on our formalism, we
propose an approach to compute the eigenenergies of the low-lying scattering
states of the relative motion of the colliding nuclei as a function of the
oscillator strength of the confining potential. Utilizing the modified
effective range expansion, we extrapolate the elastic scattering phase shift of
the colliding nuclei from these eigenenergies to the limit when the external
potential vanishes. In our hybrid approach, we leverage the advantage of
quantum computing to solve for these eigenenergies from a set of many-nucleon
Hamiltonian eigenvalue problems. These eigenenergies are inputs to classical
computers to obtain the phase shift. We demonstrate our framework with two
simple problems, where we implement the rodeo algorithm to solve the relevant
eigenenergies with the IBM Qiskit quantum simulator. The results of both the
spectra and the elastic scattering phase shifts agree well with other
theoretical results.
