A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green’s functions on the quantum hardware. Particle decay rates and two particle scattering cross sections are extracted from the imaginary parts of the Green’s function. A 0 + 1 dimensional implementation of this method is demonstrated on IBM’s superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.