  Previous studies have related surface temperature maps, obtained with the
Doppler imaging (DI) technique, of LQ Hya with long-term photometry. We compare
surface magnetic field maps, obtained with the Zeeman Doppler imaging (ZDI)
technique, with contemporaneous photometry, with the aim of quantifying the
star's magnetic cycle characteristics. We inverted Stokes IV spectropolarimetry
into magnetic field and surface brightness maps using a tomographic inversion
code that models high signal-to-noise ratio mean line profiles produced by the
least squares deconvolution (LSD) technique. The magnetic field and surface
brightness maps reveal similar patterns to previous DI and ZDI studies:
non-axisymmetric polar magnetic field structure, void of fields at
mid-latitudes, and a complex structure in the equatorial regions. There is a
weak but clear tendency of the polar structures to be linked with strong radial
field and the equatorial ones with the azimuthal. We find a polarity reversal
in the radial field between 2016 and 2017 coincident with an activity minimum
seen in the long-term photometry. The inverted field strengths cannot easily be
related with the observed spottedness, but we find that they are partially
connected with the retrieved field complexity. Comparing to global
magnetoconvection models for rapidly rotating young Suns, this field topology
and dominance of the poloidal field component could be explained by a turbulent
dynamo, where differential rotation does not play a major role (so called
alpha^2 Omega or alpha^2 dynamos), and axi- and non-axisymmetric modes are
excited simultaneously. The complex equatorial magnetic field structure could
arise from the twisted (helical) wreaths often seen in these simulations, while
the polar feature would be connected to the mostly poloidal non-axisymmetric
component having a smooth spatial structure.
