  We present an experimental investigation of coherent crosstalk cancellation
methods for light delivered to a linear ion chain cryogenic quantum register.
The ions are individually addressed using focused laser beams oriented
perpendicular to the crystal axis, which are created by imaging each output of
a multi-core photonic-crystal fibre waveguide array onto a single ion. The
measured nearest-neighbor native crosstalk intensity of this device for ions
spaced by 5 $\mu$m is found to be $\sim 10^{-2}$. We show that we can suppress
this intensity crosstalk from waveguide channel coupling and optical
diffraction effects by a factor $>10^3$ using cancellation light supplied to
neighboring channels which destructively interferes with the crosstalk. We
measure a rotation error per gate on the order of $\epsilon_{x} \sim 10^{-5}$
on spectator qubits, demonstrating a suppression of crosstalk error by a factor
of $> 10^2$. We compare the performance to composite pulse methods for
crosstalk cancellation, and describe the appropriate calibration methods and
procedures to mitigate phase drifts between these different optical paths,
including accounting for problems arising due to pulsing of optical modulators.
