Measurement-induced entanglement phase transitions in monitored quantum systems are a striking example of exotic dynamical phases in open quantum systems. However, probing these transitions in large systems requires an exponential number of experimental repetitions. This paper proposes using a neural network decoder to determine the state of reference qubits, conditioned on measurement outcomes, providing a more efficient method to probe these phase transitions. The entanglement phase transition manifests as a change in the learnability of the decoder function. The approach is studied in Clifford and Haar random circuits, demonstrating scalability and applicability to generic experiments.

Hossein Dehghani, Ali Lavasani, Mohammad Hafezi, Michael J. Gullans