Relativistic quantum field theory describes all of the fundamental interactions in Nature, with the possible exception of gravity, I will describe and analyze a quantum algorithm for simulating real-time evolution in an interacting massive scalar quantum field theory in four or fewer spacetime dimensions. The run time of the algorithm scales polynomially in the particle number, the energy, and the desired precision. Hence the algorithm achieves an exponential speedup relative to the best existing classical algorithms. This result supports the conjecture that all physical processes in Nature can be simulated efficiently using a universal quantum computer. Based on joint work with Stephen Jordan and Keith Lee.