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Quantum field theory provides the framework for the most fundamental physicaltheories to be confirmed experimentally and has enabled predictions ofunprecedented precision. However, calculations of physical observables oftenrequire great computational complexity and can generally be performed only whenthe interaction strength is weak. A full understanding of the foundations andrich consequences of quantum field theory remains an outstanding challenge. Wedevelop a quantum algorithm to compute relativistic scattering amplitudes inmassive phi-fourth theory in spacetime of four and fewer dimensions. Thealgorithm runs in a time that is polynomial in the number of particles, theirenergy, and the desired precision, and applies at both weak and strongcoupling. Thus, it offers exponential speedup over existing classical methodsat high precision or strong coupling.

Quantum Computation of Scattering in Scalar Quantum Field Theories