  By exploiting the exotic quantum states of a probe, it is possible to realize
efficient sensors that are attractive for practical metrology applications and
fundamental studies. Similar to other quantum technologies, quantum sensing is
suffering from noises and thus the experimental developments are hindered.
Although theoretical schemes based on quantum error correction (QEC) have been
proposed to combat noises, their demonstrations are prevented by the stringent
experimental requirements, such as perfect quantum operations and the
orthogonal condition between the sensing interaction Hamiltonian and the noise
Lindbladians. Here, we report an experimental demonstration of a quantum
enhancement in sensing with a bosonic probe with different encodings, by
exploring the large Hilbert space of the bosonic mode and developing both the
approximate QEC and the quantum jump tracking approaches. In a practical
radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which
reaches $9.1\times10^{-4}\,\mathrm{Hz}^{-1/2}$ when measuring the excitation
population of a receiver mode. Our results demonstrate the potential of quantum
sensing with near-term quantum technologies, not only shedding new light on the
quantum advantage of sensing by revealing its difference from other quantum
applications, but also stimulating further efforts on bosonic quantum
technologies.
