  Quantum simulation holds promise of enabling a complete description of
high-energy scattering processes rooted in gauge theories of the Standard
Model. A first step in such simulations is preparation of interacting hadronic
wave packets. To create the wave packets, one typically resorts to adiabatic
evolution to bridge between wave packets in the free theory and those in the
interacting theory, rendering the simulation resource intensive. In this work,
we construct a wave-packet creation operator directly in the interacting theory
to circumvent adiabatic evolution, taking advantage of resource-efficient
schemes for ground-state preparation, such as variational quantum eigensolvers.
By means of an ansatz for bound mesonic excitations in confining gauge
theories, which is subsequently optimized using classical or quantum methods,
we show that interacting mesonic wave packets can be created efficiently and
accurately using digital quantum algorithms that we develop. Specifically, we
obtain high-fidelity mesonic wave packets in the $Z_2$ and $U(1)$ lattice gauge
theories coupled to fermionic matter in 1+1 dimensions. Our method is
applicable to both perturbative and non-perturbative regimes of couplings. The
wave-packet creation circuit for the case of the $Z_2$ lattice gauge theory is
built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using
13 qubits and up to 308 entangling gates. The fidelities agree well with
classical benchmark calculations after employing a simple symmetry-based
noise-mitigation technique. This work serves as a step toward quantum computing
scattering processes in quantum chromodynamics.
