  We present methods for interpolating between the 1-D flux power spectrum of
the Lyman-$\alpha$ forest, as output by cosmological hydrodynamic simulations.
Interpolation is necessary for cosmological parameter estimation due to the
limited number of simulations possible. We construct an emulator for the
Lyman-$\alpha$ forest flux power spectrum from $21$ small simulations using
Latin hypercube sampling and Gaussian process interpolation. We show that this
emulator has a typical accuracy of 1.5% and a worst-case accuracy of 4%, which
compares well to the current statistical error of 3 - 5% at $z < 3$ from BOSS
DR9. We compare to the previous state of the art, quadratic polynomial
interpolation. The Latin hypercube samples the entire volume of parameter
space, while quadratic polynomial emulation samples only lower-dimensional
subspaces. The Gaussian process provides an estimate of the emulation error and
we show using test simulations that this estimate is reasonable. We construct a
likelihood function and use it to show that the posterior constraints generated
using the emulator are unbiased. We show that our Gaussian process emulator has
lower emulation error than quadratic polynomial interpolation and thus produces
tighter posterior confidence intervals, which will be essential for future
Lyman-$\alpha$ surveys such as DESI.
