Revision 1

Superseded · first revision · record

Title: Observing the measurement-induced transition without exponential postselection
Plain: Seeing the transition directly requires repeating the same random set of measurement outcomes, which happens with exponentially small probability. A way to detect it in generic circuits with resources that grow only polynomially with size is not established.
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.
Settled by: An efficient detection protocol with proof and a demonstration on hardware, or a lower bound on sample complexity.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
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.
Posed since: (empty)