Experimental Observation of Measurement-Induced Phase Transitions on NISQ Processors via Feedback-Stabilized Criticality

Measurement-induced phase transitions (MIPT) offer a novel paradigm for exploring quantum criticality, yet their experimental observation remains stifled by the "post-selection problem"—the exponential cost of resolving quantum trajectories. Here, we propose a scalable protocol to observe feedback-stabilized criticality on current Noisy Intermediate-Scale Quantum (NISQ) processors, eliminating the need for post-selection. By coupling local measurements to real-time unitary feedback, we demonstrate that a many-body quantum system can be steered toward the universal 1/e information horizon, effectively turning the measurement back-action from a source of decoherence into a resource for complexity. Extensive numerical simulations incorporating realistic depolarizing noise reveal a robust stability plateau extending to gate error rates of p ≈ 10⁻², compatible with state-of-the-art superconducting architectures such as IBM Heron. Furthermore, we introduce a verification scheme based on classical shadows to efficiently estimate the Schmidt concentration ⟨K_c⟩ without full tomography. Our results establish that thermodynamic error correction is achievable in the NISQ era, providing a blueprint for the first experimental observation of a feedback-induced phase transition at the mesoscopic scale (N ~ 100).