  Particles produced in high energy collisions that are charged under one of
the fundamental forces will radiate proportionally to their charge, such as
photon radiation from electrons in quantum electrodynamics. At sufficiently
high energies, this radiation pattern is enhanced collinear to the initiating
particle, resulting in a complex, many-body quantum system. Classical Markov
Chain Monte Carlo simulation approaches work well to capture many of the
salient features of the shower of radiation, but cannot capture all quantum
effects. We show how quantum algorithms are well-suited for describing the
quantum properties of final state radiation. In particular, we develop a
polynomial time quantum final state shower that accurately models the effects
of intermediate spin states similar to those present in high energy electroweak
showers. The algorithm is explicitly demonstrated for a simplified quantum
field theory on a quantum computer.
