A new quantum algorithm for preparing the initial state (wavepackets) of a quantum field theory scattering simulation is introduced. This method extends recent techniques for preparing W states using mid-circuit measurement and feedforward to efficiently create wavepackets. The required circuit depth is independent of wavepacket size, representing a superexponential improvement over previous methods. Explicit examples are provided for one-dimensional Ising field theory, scalar field theory, the Schwinger model, and two dimensional Ising field theory. The circuits that prepare wavepackets in one-dimensional Ising field theory are used to simulate scattering on 100 qubits of IBM’s quantum computer ibm_marrakesh. Quantum simulations are performed at a center of mass energy above inelastic threshold, and measurements of the energy density in the post-collision state reveal the production of new particles. A novel error mitigation strategy based on energy conservation enables accurate results to be extracted from circuits with up to 6,412 two-qubit gates. The prospects for a near-term quantum advantage in simulations of scattering are discussed.