  Fully general-relativistic binary-neutron-star (BNS) merger simulations with
quark-hadron crossover (QHC) equations of state (EOSs) are studied for the
first time. In contrast to EOSs with purely hadronic matter or with a
first-order quark-hadron phase transition (1PT), in the transition region QHC
EOSs show a peak in sound speed, and thus a stiffening. We study the effects of
such stiffening in the merger and post-merger gravitational (GW) signals.
Through simulations in the binary-mass range $2.5 < M/M_{\odot} < 2.75$,
characteristic differences due to different EOSs appear in the frequency of the
main peak of the post-merger GW spectrum ($f_2$), extracted through Bayesian
inference. In particular, we found that (i) for lower-mass binaries, since the
maximum baryon number density ($n_{\rm max}$) after the merger stays below
$3\text{--}4$ times the nuclear-matter density ($n_0$), the characteristic
stiffening of the QHC models in that density range results in a lower $f_2$
than that computed for the underlying hadronic EOS and thus also than that for
EOSs with a 1PT, (ii) for higher-mass binaries, where $n_{\rm max}$ may exceed
$4\text{--}5 n_0$ depending on the EOS model, whether $f_2$ in QHC models is
higher or lower than that in the underlying hadronic model depends on the
height of the sound-speed peak. Comparing the values of $f_2$ for different
EOSs and BNS masses gives important clues on how to discriminate different
types of quark dynamics in the high-density end of EOSs and is relevant to
future kilohertz GW observations with third-generation GW detectors.
