  Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are
assumed to be limited by the typical average observational cadence of
$1/(2~{\rm weeks})$ for a single pulsar to GW frequencies $\lesssim 4\times
10^{-7}$ Hz. We show that this assumption is incorrect and that a PTA can
detect signals with much higher frequencies, which are preserved in the data
due to aliasing, by exploiting asynchronous observations from multiple pulsars.
This allows an observation strategy that is scalable to future large-scale PTAs
containing $O(10^3)$ pulsars, enabled by the Five-hundred meter Aperture
Spherical Telescope and the Square Kilometer Array, without requiring a higher
per-pulsar observation cadence. We show that higher frequency GW observations,
reaching up to $4\times 10^{-4}$ Hz with an SKA-era PTA, have significant
astrophysical implications, such as (i) a three orders of magnitude better
constraint than current high-cadence observations on GW strain in the
$[10,400]$ $\mu{\rm Hz}$ band, and (ii) sensitive tests of the no-hair theorem
in the mass range of supermassive black hole binaries using their inspiral,
merger, and ringdown signals.
