Measurement-induced phase transitions in quantum automaton circuits

Understand

We study the entanglement dynamics in a generic quantum automaton circuit subjected to projective measurements.

• We design an efficient algorithm which not only allows us to perform large scale simulation for the R\'enyi entropy but also provides a physical picture for the entanglement dynamics, which can be interpreted in terms of a classical bit-string model which belongs to the directed percolation universality class.
• We study the purification dynamics of a state formed by EPR pairs, and the growth of entanglement starting from a product state.
• In both cases, we verify numerically that the dynamics is in the universality class of classical directed percolation.