  Quantum field theory provides the framework for the most fundamental physical
theories to be confirmed experimentally and has enabled predictions of
unprecedented precision. However, calculations of physical observables often
require great computational complexity and can generally be performed only when
the interaction strength is weak. A full understanding of the foundations and
rich consequences of quantum field theory remains an outstanding challenge. We
develop a quantum algorithm to compute relativistic scattering amplitudes in
massive phi-fourth theory in spacetime of four and fewer dimensions. The
algorithm runs in a time that is polynomial in the number of particles, their
energy, and the desired precision, and applies at both weak and strong
coupling. Thus, it offers exponential speedup over existing classical methods
at high precision or strong coupling.
