Nonstabilizerness and Error Resilience in Noisy Quantum Circuits

We investigate how noise impacts nonstabilizerness-a key resource for quantum advantage-in many-body qubit systems. While noise typically degrades quantum resources, we show that amplitude damping, a nonunital channel, can generate or enhance nonstabilizerness, whereas depolarizing noise provably cannot. In an encoding-decoding protocol, we find that, unlike in the coherent-noise case, a sharp decoding fidelity transition is not accompanied by a transition in nonstabilizerness. Although amplitude damping locally injects nonstabilizerness, this resource is washed out at the collective level after encoding, decoding, and postselection. Our results reveal that realistic incoherent noise can suppress many-body nonstabilizerness criticality even while generating it microscopically.