  Quantum metrology employs quantum resources to enhance the measurement
sensitivity beyond that can be achieved classically. While multi-photon
entangled NOON states can in principle beat the shot-noise limit and reach the
Heisenberg limit, high NOON states are difficult to prepare and fragile to
photon loss which hinders it from reaching unconditional quantum metrological
advantages. Here, we combine the idea of unconventional nonlinear
interferometers and stimulated emission of squeezed light, previously developed
for photonic quantum computer Jiuzhang, to propose and realize a new scheme
that achieves a scalable, unconditional, and robust quantum metrological
advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in
the Fisher information extracted per photon, without discounting for photon
loss and imperfections, which outperforms ideal 5-NOON states. The
Heisenberg-limited scaling, the robustness to external photon loss, and the
ease-to-use of our method make it applicable in practical quantum metrology at
low photon flux regime.
