Monitored random unitary circuits with intermittent measurements can host a phase transition between a pure and a mixed phase with different entanglement entropy behaviors with the system size. Recently, it was demonstrated that these phase transitions can be locally probed via entangling reference qubits to the quantum circuit and studying the purification dynamics of the reference qubits. After disentangling from the circuit, the state of the reference qubit can be determined according to the measurement outcomes of the qubits in the circuit. In this work, we leverage modern machine learning tools to decode the state of the reference qubits. In particular, by considering circuits with given random operators and measurement locations, we design a neural network decoder to efficiently determine the state of the reference qubit based on the measurement records.  Next, after studying the complexity of our neural network decoders, we demonstrate that entanglement entropy scaling phase transition can be translated into the learnability of the decoder function. Finally, we show that our learning procedure is transferable from smaller circuits to larger circuit with hundreds of qubits which proves the scalability of our method.

(Pizza and refreshments will be served after the talk.)