In the era of noisy intermediate scale quantum (NISQ) hardware, digital quantum computers are limited to shallow circuits on the order of a thousand layers due to system noise and qubit decoherence. Thus, every step of a simulation must be as efficient as possible. Modifying the recent Givens Rotation state preparation by Chai et al and ladder operator block encoding method by Simon et al, we propose a scattering state preparation method that approximates the fermionic wave packets by localizing them in space, reducing circuit depth by nearly half, while also preserving fermionic anti-commutation relations. Using MPS simulations, we show that these approximated wave packets approach the exact wave packets in weakly interacting critical theories; and then show its immediate application on modern day hardware with IonQ's Forte 1 machine.