Simulating Scattering of Composite Particles

We develop a non-perturbative approach to simulating scattering on classical and quantum computers, in which the initial and final states contain a fixed number of composite particles. The construction is designed to mimic a particle collision, wherein two composite particles are brought in contact. The initial states are assembled via consecutive application of operators creating eigenstates of the interacting theory from vacuum. These operators are defined with the aid of the M{\o}ller wave operator, which can be constructed using such methods as adiabatic state preparation or double commutator flow equation. The approach is well-suited for studying strongly coupled systems in both relativistic and non-relativistic settings. For relativistic systems, we employ the language of light-front quantization, which has been previously used for studying the properties of individual bound states, as well as for simulating their scattering in external fields, and is now adopted to the studies of scattering of bound state systems. For simulations on classical computers, we describe an algorithm for calculating exact (in the sense of a given discretized theory) scattering probabilities, which has cost (memory and time) exponential in momentum grid size. Such calculations may be interesting in their own right and can be used for benchmarking results of a quantum simulation algorithm, which is the main application of the developed framework. We illustrate our ideas with an application to the $\phi^4$ theory in $1+1\rm D$.