  Accurate predictions for the non-linear matter power spectrum are needed to
confront theory with observations in current and near future weak lensing and
galaxy clustering surveys. We propose a computationally cheap method to create
an emulator for modified gravity models by utilizing existing emulators for
$\Lambda$CDM. Using a suite of $N$-body simulations we construct a fitting
function for the enhancement of both the linear and non-linear matter power
spectrum in the commonly studied Hu-Sawicki $f(R)$ gravity model valid for
wave-numbers $k \lesssim 5-10\, h\text{Mpc}^{-1}$ and redshifts $z \lesssim 3$.
We show that the cosmology dependence of this enhancement is relatively weak so
that our fit, using simulations coming from only one cosmology, can be used to
get accurate predictions for other cosmological parameters. We also show that
the cosmology dependence can, if needed, be included by using linear theory,
approximate $N$-body simulations (such as COLA) and semi-analytical tools like
the halo model. Our final fit can easily be combined with any emulator or
semi-analytical models for the non-linear $\Lambda$CDM power spectrum to
accurately, and quickly, produce a non-linear power spectrum for this
particular modified gravity model. The method we use can be applied to fairly
cheaply construct an emulator for other modified gravity models. As an
application of our fitting formula we use it to compute Fisher-forecasts for
how well galaxy clustering and weak lensing in a Euclid-like survey will be at
constraining modifications of gravity.
