Approaching the critical point through an exact ground-state evolution

We investigate critical quantum metrology in a system where a qubit is dispersively coupled to a parametrically driven bosonic field. By engineering a counterdiabatic driving Hamiltonian under realistic physical constraints, we demonstrate a high-fidelity preparation of quantum states near a quantum phase transition. Our protocol extends the application of criticality-enhanced metrology to the short-time regime, offering a significant advantage over nonassisted protocols. The metrological precision is quantified by the quantum Fisher information (QFI) and the signal-to-noise ratio (SNR). Even with a constrained driving strength, numerical simulations reveal a QFI enhancement factor exceeding 10^{3} and an SNR enhancement of over 10^{6} in this regime. This work opens a promising avenue for critical quantum metrology.