  We present the first numerically stable nonlinear evolution for the
leading-order gravitational effective field theory (Quadratic Gravity) in the
spherically-symmetric sector. The formulation relies on (i) harmonic gauge to
cast the evolution system into quasi-linear form (ii) the Cartoon method to
reduce to spherical symmetry in keeping with harmonic gauge, and (iii)
order-reduction to 1st-order (in time) by means of introducing auxiliary
variables. Well-posedness of the respective initial-value problem is
numerically confirmed by evolving randomly perturbed flat-space and black-hole
initial data. Our study serves as a proof-of-principle for the possibility of
stable numerical evolution in the presence of higher derivatives.
