Quantum spin systems can demonstrate a variety of interesting quantum phenomena, ranging from soliton lattices to quantum spin liquids, with a potential to constitute key elements in various quantum applications. Inelastic scattering experiments, such as using inelastic neutron scattering (INS) and NMR, provide key insights into the dynamics of spins inside quantum magnets. To understand such spin dynamics, we compute the magnetic neutron cross-section on qubit-based hardware extending the prescription laid in Nature Phys. 15, 455 (2019). We have utilized the IBM quantum devices to simulate the time evolution of different Hamiltonians acting on an initial state for spin-½ systems, starting from 2-spin systems and extending above, and have been able to measure the coefficients of the correlation functions. In order to mitigate the backend noise and to capture longer time dynamics, we use a variational fast-forwarding (VFF) ansatz, and compare the results to that of trotterization, as well as compare between direct (ancilla qubit-free circuits) and indirect (circuits including ancilla qubit) measurements. We end with ongoing ideas to expand to larger spin networks to emulate scattering results from INS measurements. *The work is supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE) led by Oak Ridge National Laboratory (ORNL). The authors also acknowledge support from the IBM Quantum Summer Internship.