Hamiltonian simulation of lattice gauge theories (LGTs) is a non-perturbative method of numerically solving gauge theories that offers novel avenues for studying scattering processes in gauge theories. With the advent of quantum computers, Hamiltonian simulation of LGTs has become a reality. Simulating scattering on quantum computers requires the preparation of initial scattering states in the interacting theory on the quantum hardware. Current state preparation methods involve bridging the scattering states in the free theory to the ones in the interacting theory adiabatically. Such quantum algorithms have limitations when applied to LGTs, and they tend to be computational resource intensive, rendering their implementation a challenge on the noisy intermediate-scale quantum (NISQ) era devices. In this work, we propose a wave packet state preparation algorithm for a 1+1D Z2 LGT coupled to dynamical matter. We show how this algorithm circumvents the adiabatic process by building and implementing the wave packet creation operators directly in the interacting theory using an optimized ansatz consisting of hadronic degrees of freedom in the confined Z2 LGT. Moreover, we numerically confirm the validity of this ansatz for a U(1) LGT in 1+1D. Finally, we demonstrate the viability of our algorithm for NISQ devices by comparing the classical simulation with the results obtained using the Quantinuum H1-1 quantum computer upon a simple symmetry-based noise mitigation technique.
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