Quantum Algorithms for Quantum Field Theories

TL;DR

This paper introduces a quantum algorithm capable of efficiently computing scattering probabilities in quantum field theories, offering exponential speedup over classical methods especially in strong-coupling regimes.

Contribution

The authors develop a quantum algorithm for relativistic scattering in quantum field theories that is efficient across different coupling strengths and dimensions, with polynomial runtime.

Findings

Achieves exponential speedup in strong-coupling regimes

Runs in polynomial time relative to particles, energy, and precision

Applicable to quantum field theories in four or fewer dimensions

Abstract

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.