Towards Quantum Simulation of Bound States Scattering

The last years have seen a 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 for preparation of states of composite particles. This is the first step towards 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 depending on the state being prepared. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time.