Quantum Algorithms for Quantum Field Theories

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