  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.
