  We investigate the prospects for using the weak lensing bispectrum alongside
the power spectrum to control systematic uncertainties in a Euclid-like survey.
Three systematic effects are considered: the intrinsic alignment of galaxies,
uncertainties in the means of tomographic redshift distributions, and
multiplicative bias in the measurement of the shear signal. We find that the
bispectrum is very effective in mitigating these systematic errors. Varying all
three systematics simultaneously, a joint power spectrum and bispectrum
analysis reduces the area of credible regions for the cosmological parameters
$\Omega_\mathrm{m}$ and $\sigma_8$ by a factor of 90 and for the two parameters
of a time-varying dark energy equation of state by a factor of almost 20,
compared with the baseline approach of using the power spectrum alone and of
imposing priors consistent with the accuracy requirements specified for Euclid.
We also demonstrate that including the bispectrum self-calibrates all three
systematic effects to the stringent levels required by the forthcoming
generation of weak lensing surveys, thereby reducing the need for external
calibration data.
