  Doubly heavy tetraquark states are the prime candidates for tightly bound
exotic states. We present a systematic study of the mass spectra of the
$S$-wave doubly heavy tetraquark states $QQ\bar{q}\bar{q}$ ($q=u, d, s$ and
$Q=c, b$) with different quantum numbers $J^P=0^+$, $1^+$, and $2^+$ in the
framework of the improved chromomagnetic interaction (ICMI) model. The
parameters in the ICMI model are obtained by fitting the conventional hadron
spectra and are used directly to predict the masses of the tetraquark states.
For heavy quarks, the uncertainties of the parameters are obtained by comparing
the masses of doubly and triply heavy baryons with those given by lattice QCD,
QCD sum rules, and potential models. Several compact and stable bound states
are found in both the doubly charmed and doubly bottomed tetraquark systems.
The predicted mass of the $cc\bar u\bar d$ state is consistent with the recent
measurement from the LHCb collaboration.
