  It has been suggested that some classes of luminous supernovae (SNe) and
gamma-ray bursts (GRBs) are driven by newborn magnetars. Fast-rotating
proto-neutron stars have also been of interest as potential sources of
gravitational waves (GWs). We show that for a range of rotation periods and
magnetic fields, hard X rays and GeV gamma rays provide us with a promising
probe of pulsar-aided SNe. It is observationally known that young pulsar wind
nebulae (PWNe) in the Milky Way are very efficient lepton accelerators. We
argue that, if embryonic PWNe satisfy similar conditions at early stages of SNe
(in ~1-10 months after the explosion), external inverse-Compton emission via
upscatterings of SN photons is naturally expected in the GeV range as well as
broadband synchrotron emission. To fully take into account the Klein-Nishina
effect and two-photon annihilation process that are important at early times,
we perform detailed calculations including electromagnetic cascades. Our
results suggest that hard X-ray telescopes such as NuSTAR can observe such
early PWN emission by followup observations in months-to-years. GeV gamma rays
may also be detected by Fermi for nearby SNe, which serve as counterparts of
these GW sources. Detecting the signals will give us an interesting probe of
particle acceleration at early times of PWNe, as well as clues to driving
mechanisms of luminous SNe and GRBs. Since the Bethe-Heitler cross section is
lower than the Thomson cross section, gamma rays would allow us to study
subphotospheric dissipation. We encourage searches for high-energy emission
from nearby SNe, especially Type Ibc SNe including super-luminous objects.
