  Simulating the full dynamics of a quantum field theory over a wide range of
energies requires exceptionally large quantum computing resources. Yet for many
observables in particle physics, perturbative techniques are sufficient to
accurately model all but a constrained range of energies within the validity of
the theory. We demonstrate that effective field theories (EFTs) provide an
efficient mechanism to separate the high energy dynamics that is easily
calculated by traditional perturbation theory from the dynamics at low energy
and show how quantum algorithms can be used to simulate the dynamics of the low
energy EFT from first principles. As an explicit example we calculate the
expectation values of vacuum-to-vacuum and vacuum-to-one-particle transitions
in the presence of a time-ordered product of two Wilson lines in scalar field
theory, an object closely related to those arising in EFTs of the Standard
Model of particle physics. Calculations are performed using simulations of a
quantum computer as well as measurements using the IBMQ Manhattan machine.
