  The real time evolution of quantum field theory models can be calculated
order by order in perturbation theory. For $\lambda \phi^4$ models, the
perturbative series have a zero radius of convergence which in part motivated
the design of digitized versions suitable for quantum computing. In agreement
with general arguments suggesting that a large field cutoff modifies Dyson's
reasoning and improves convergence properties, we show that the harmonic
digitizations of $\lambda \phi^4$ lattice field theories lead to weak coupling
expansions with a finite radius of convergence. Similar convergence properties
are found for strong coupling expansions. We compare the resources needed to
calculate the real-time evolution of the digitized models with perturbative
expansions to those needed to do so with universal quantum computers. Unless
new approximate methods can be designed to calculate long perturbative series
for large systems efficiently, it appears that the use of universal quantum
computers with digitizations involving a few qubits per site has the potential
for more efficient calculations of the real-time evolution for large systems at
intermediate coupling.
