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A way to detect it in generic circuits with resources that grow only polynomially with size is not established.","posed_since":"","precise":"For non-Clifford monitored circuits on $N$ qubits under Born-rule measurements, find an estimator that detects $p_c$ with $\\operatorname{poly}(N)$ samples and $\\operatorname{poly}(N)$ classical processing, or prove that every such probe needs $\\operatorname{exp}(N)$ resources. Known probes use Clifford circuits, require classically simulating the circuit (cross-entropy benchmark of Li, Zou, Glorioso, Altman and Fisher, PRL 130, 220404, 2023), or postselect.","problem_ref":null,"references":"","settled_by":"An efficient detection protocol with proof and a demonstration on hardware, or a lower bound on sample complexity.","status_note":"Google Quantum AI (Nature 2023) observed measurement-induced entanglement signatures on a processor of about 70 qubits (approximate) using decoding methods; the general question is open.","title":"Observing the measurement-induced transition without exponential 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