  Fast radio bursts (FRBs) are bright flashes observed typically at GHz
frequencies with millisecond duration, whose origin is likely extragalactic.
Their nature remains mysterious, motivating searches for counterparts at other
wavelengths. FRB 121102 is so far the only source known to repeatedly emit FRBs
and is associated with a host galaxy at redshift $z \simeq 0.193$. We conducted
simultaneous observations of FRB 121102 with the Arecibo and MAGIC telescopes
during several epochs in 2016--2017. This allowed searches for
millisecond-timescale burst emission in very-high-energy (VHE) gamma rays as
well as the optical band. While a total of five FRBs were detected during these
observations, no VHE emission was detected, neither of a persistent nature nor
burst-like associated with the FRBs. The average integral flux upper limits
above 100 GeV at 95% confidence level are $6.6 \times 10^{-12}~\mathrm{photons\
cm^{-2}\ s^{-1}}$ (corresponding to luminosity $L_{\rm VHE} \lesssim
10^{45}~\mathrm{erg\ s^{-1}}$) over the entire observation period, and $1.2
\times 10^{-7}~ \mathrm{photons\ cm^{-2}\ s^{-1}}$ ($L_{\rm VHE} \lesssim
10^{49}~\mathrm{erg\ s^{-1}}$) over the total duration of the five FRBs. We
constrain the optical U-band flux to be below 8.6 mJy at 5-$\sigma$ level for
1-ms intervals around the FRB arrival times. A bright burst with U-band flux
$29~\mathrm{mJy}$ and duration $\sim 12$ ms was detected 4.3 s before the
arrival of one FRB. However, the probability of spuriously detecting such a
signal within the sampled time space is 1.5% (2.2 $\sigma$, post-trial), i.e.
consistent with the expected background. We discuss the implications of the
obtained upper limits for constraining FRB models.
