  We discuss the concept of typicality of quantum states at quantum-critical
points, using projector Monte Carlo simulations of an $S=1/2$ bilayer
Heisenberg antiferromagnet as an illustration. With the projection (imaginary)
time $\tau$ scaled as $\tau =aL^z$, $L$ being the system length and $z$ the
dynamic critical exponent (which takes the value $z=1$ in the bilayer model
studied here), a critical point can be identified which asymptotically flows to
the correct location and universality class with increasing $L$, independently
of the prefactor $a$ and the initial state. Varying the proportionality factor
$a$ and the initial state only changes the cross-over behavior into the
asymptotic large-$L$ behavior. In some cases, choosing an optimal factor $a$
may also lead to the vanishing of the leading finite-size corrections. The
observation of typicality can be used to speed up simulations of quantum
criticality, not only within the Monte Carlo approach but also with other
numerical methods where imaginary-time evolution is employed, e.g., tensor
network states, as it is not necessary to evolve fully to the ground state but
only for sufficiently long times to reach the typicality regime.
