The ability to extend the lifetime of a logical qubit beyond that of the best physical qubit available within the same system, i.e., the break-even point, is a prerequisite for building practical quantum computers. So far, this point has been exceeded through active quantum error correction (QEC) protocols, where a logical error is corrected by measuring its syndrome and then performing an adaptive correcting operation. Autonomous QEC (AQEC), without the need for such resource-consuming measurement-feedback control, has been demonstrated in several experiments, but none of which has unambiguously reached the break-even point. Here, we present an unambiguous demonstration of beyond-break-even AQEC in a circuit quantum electrodynamics system, where a photonic logical qubit encoded in a superconducting microwave cavity is protected against photon loss through autonomous error correction, enabled by engineered dissipation. Under the AQEC protection, the logical qubit achieves a lifetime surpassing that of the best physical qubit available in the system by 18%. We further employ this AQEC protocol to enhance the precision for measuring a slight frequency shift, achieving a metrological gain of 6.3 dB over that using the most robust Fock-state superposition. These results illustrate that the demonstrated AQEC procedure not only represents a crucial step towards fault-tolerant quantum computation but also offers advantages for building robust quantum sensors.

Fock states with a well-defined number of photons in an oscillator have shown a wide range of applications in quantum information science. Nonetheless, their usefulness has been marred by single and multiple photon losses due to unavoidable environment-induced dissipation. Though several dissipation engineering methods have been developed to counteract the leading single-photon loss error, averting multiple photon losses remains elusive. Here, we experimentally demonstrate a dissipation engineering method that autonomously stabilizes multi-photon Fock states against losses of multiple photons using a cascaded selective photon-addition operation in a superconducting quantum circuit. Through measuring the photon-number populations and Wigner tomography of the oscillator states, we observe a prolonged preservation of nonclassical Wigner negativities for the stabilized Fock states $\vert N\rangle$ with $N=1,2,3$ for a duration of about 10 ms. Furthermore, the dissipation engineering method demonstrated here also facilitates the implementation of a non-unitary operation for resetting a binomially-encoded logical qubit. These results highlight potential applications in error-correctable quantum information processing against multi-photon-loss errors.

Quantum metrology uses non-classical states, such as Fock states with a specific number of photons, to achieve an advantage over classical sensing methods. Typically, quantum metrological performance can be enhanced by increasing the involved excitation numbers, for example, by using large-photon-number Fock states. However, manipulating these states and demonstrating a quantum metrological advantage is experimentally challenging. Here we present an efficient method for generating large Fock states approaching 100 photons within a superconducting microwave cavity through the development of a programmable photon number filter. Using these states in displacement and phase measurements, we demonstrate quantum-enhanced metrology approaching the Heisenberg scaling for 40-photon Fock states and achieve a maximum metrological gain of up to 14.8 dB, highlighting the metrological advantages of large Fock states. Our study could be readily extended to mechanical and optical systems, promising potential applications in weak force detection and dark matter searches. Non-classical states with a large, definite number of photons can now be produced in a superconducting cavity and used for quantum-enhanced sensing.