  Quantum error correction provides a path to large-scale quantum computers,
but is built on challenging assumptions about the characteristics of the
underlying errors. In particular, the mathematical assumption of statistically
independent errors in quantum logic operations is at odds with realistic
environments where error sources may exhibit strong temporal and spatial
correlations. We present experiments using trapped ions to demonstrate that the
use of dynamically corrected gates (DCGs), generally considered for the
reduction of error magnitudes, can also suppress error correlations in space
and time throughout quantum circuits. We present a first-principles analysis of
the manifestation of error correlations in randomized benchmarking, and
validate this model through experiments performed using engineered errors. We
find that standard DCGs can reduce error correlations by $\sim50\times$, while
increasing the magnitude of uncorrelated errors by a factor scaling linearly
with the extended DCG duration compared to a primitive gate. We then
demonstrate that the correlation characteristics of intrinsic errors in our
system are modified by use of DCGs, consistent with a picture in which DCGs
whiten the effective error spectrum induced by external noise.
