  Quantum metrology has emerged as a promising avenue for surpassing the
limitations of classical mechanics in high-precision measurements. However, the
practical implementation of quantum metrology is hindered by the challenges of
manipulating exotic quantum states in large systems. Here, we propose and
demonstrate a hardware-efficient approach to achieve Heisenberg-limited quantum
metrology using large photon-number Fock states. We have developed a
programmable photon number filter that efficiently generates Fock states with
up to 100 photons in a high-quality superconducting microwave cavity. Using
these highly nontrivial states in displacement and phase measurements, we
demonstrate a precision scaling close to the Heisenberg limit and achieve a
maximum metrological gain of up to 14.8 dB. Our hardware-efficient quantum
metrology can be extended to mechanical and optical systems and provides a
practical solution for high metrological gain in bosonic quantum systems,
promising potential applications in radiometry and the search for new
particles.
