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We design and implement a quantum annealing simulation platform to observe and study dynamical processes in quantum field theory (QFT). Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof of concept, we encode a scalar field theory and measure the probability for it to tunnel from the false vacuum to the true vacuum for various tunneling times, vacuum displacements, and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a promising platform for encoding QFTs. This is the first time it has been possible to measure instanton processes across a freely chosen QFT energy barrier. We argue that this novel and flexible method to study the dynamics of quantum systems has potential application to many field theories of interest. Measurements of the dynamical behavior of such encoded field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. Soon, measurements using such a quantum annealing simulation platform could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.