  We introduce a first-order quantum-phase-transition model, which exhibits
giant sensitivity $\chi \propto N^2$ at the critical point. Exploiting this
effect, we propose a quantum critical detector (QCD) to amplify weak input
signals. The time-dynamic QCD functions by triggering a first-order dynamical
quantum phase transition in a system of spins with long-range interactions
coupled to a bosonic mode. We numerically demonstrate features of the dynamical
quantum phase transition, which leads to a time-dependent quantum gain. We also
show the linear scaling with the spin number $N$ in both the quantum gain and
the corresponding signal-to-quantum noise ratio of this QCD. Our QCD can be a
resource for metrology, weak signal amplification, and single photon detection.
