Measurement-induced phase transitions in quantum automaton circuits

TL;DR

This paper investigates how entanglement evolves in quantum automaton circuits with measurements, revealing a phase transition characterized by classical directed percolation universality.

Contribution

It introduces an efficient simulation algorithm and establishes a connection between quantum entanglement dynamics and classical directed percolation universality class.

Findings

Entanglement dynamics follow directed percolation universality.

The algorithm enables large-scale simulation of Renyi entropy.

Purification and entanglement growth exhibit critical behavior.

Abstract

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.