  The last few years have seen rapid development of applications of quantum
computation to quantum field theory. The first algorithms for quantum
simulation of scattering have been proposed in the context of scalar and
fermionic theories, requiring thousands of logical qubits. These algorithms are
not suitable to simulate scattering of incoming bound states, as the
initial-state preparation relies typically on adiabatically transforming
wavepackets of the free theory into wavepackets of the interacting theory. In
this paper we present a strategy to excite wavepackets of the interacting
theory directly from the vacuum of the interacting theory, allowing the
preparation of states of composite particles. This is the first step towards
digital quantum simulation of scattering of bound states. The approach is based
on the Haag-Ruelle scattering theory, which provides a way to construct
creation and annihilation operators of a theory in a full, nonperturbative
framework. We provide a quantum algorithm requiring a number of ancillary
qubits that is logarithmic in the size of the wavepackets, and with a success
probability vanishing at most like a polynomial in the lattice parameters and
the energy of the wavepacket. The gate complexity for a single iteration of the
circuit is equivalent to that of a time evolution for a fixed time.
Furthermore, we propose a complete protocol for scattering simulation using
this algorithm. We study its efficiency and find improvements with respect to
previous algorithms in the literature.
