A universal crossover in quantum circuits governed by a proximate classical error correction transition

Understand

We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements.

• As a starting point we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors.
• In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state vanishes.
• We show that this phase transition is in the directed percolation universality class, consistent with the fact that having zero entropy is an absorbing state of the dynamics; this classical circuit cannot generate entropy.