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Quantum field theory reconciles quantum mechanics and special relativity, andplays a central role in many areas of physics. We develop a quantum algorithmto compute relativistic scattering probabilities in a massive quantum fieldtheory with quartic self-interactions (phi-fourth theory) in spacetime of fourand fewer dimensions. Its run time is polynomial in the number of particles,their energy, and the desired precision, and applies at both weak and strongcoupling. In the strong-coupling and high-precision regimes, our quantumalgorithm achieves exponential speedup over the fastest known classicalalgorithm.

Quantum Algorithms for Quantum Field Theories