Detecting Measurement Induced Phase Transition on SuperconductingQuantum Computers with Neural Network Decoders

Measurement induced phase transition is an entanglement entropy phase transition

that can occur in monitored quantum systems composed of both unitary and non-unitary

time evolution operators which compete with each other in generating and destroying the

entanglement, respectively. An example of such systems, are hybrid quantum circuits with

random gates interspersed with random local measurements. While recently such phase

transitions have been observed in small-size random circuits, there is still no realization

of these phase transitions in large scale quantum computers. In this work, we study the

entanglement entropy of an ancilla qubits which is initially entangled to the circuit, as a

local probe that can detect this phase transition. To measure the entanglement entropy

of the ancilla qubit, we use three neural network decoders trained on the mid-circuit

measurement outcomes of the circuit and the three spins of the reference qubit at late

times. Correspondingly, the output of the neural network can determine the density matrix

of the reference qubit and its entanglement entropy as a function of time. Finally, using

the scaling behavior of the entanglement entropy of the reference qubit, we demonstrate

that the critical measurement rates of this phase transition and its critical exponents can

be estimated.