Stephen Jordan: BQP-completeness of Scattering in Quantum Field Theory

A talk by Stephen Jordan at the Workshop on Computational Complexity and High Energy Physics, hosted July 31 to August 2, 2017 by the Joint Center for Quantum Information and Computer Science at the University of Maryland. Abstract: Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we consider a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. This is joint work with Hari Krovi, Keith Lee, and John Preskill.