Entanglement structure in the volume-law phase of hybrid quantum automaton circuits

TL;DR

This paper investigates entanglement fluctuations and quantum error correction in monitored quantum automaton circuits, revealing KPZ universality in entanglement growth and emergent classical error correction properties.

Contribution

It uncovers the KPZ universality class in entanglement fluctuations and demonstrates emergent classical error correction in hybrid quantum automaton circuits.

Findings

Entanglement entropy fluctuations follow KPZ universality.

The model exhibits different code distances for two error types.

Classical particle dynamics show error correction ability.

Abstract

We study entanglement fluctuations and quantum error correction in the weakly monitored volume-law phase of quantum automaton circuits subject to repeated local measurements. We numerically observe that the entanglement entropy exhibits strong fluctuation with the exponent close to the ``growth exponent'' of the Kardar-Parisi-Zhang (KPZ) universality class, the same as other local random circuits studied previously. We also investigate the dynamically generated quantum error correction code in the purification process and show that this model has different contiguous code distances for two types of errors that exhibit similar sublinear power-law scaling. We give an interpretation of these results by mapping them to various quantities in a classical particle model. We demonstrate that the subleading correction term of the entanglement entropy and the sublinear power-law scaling of the contiguous code distance in the volume-law phase are both the emergent phenomena of the hybrid random dynamics. Finally, we show that this classical particle dynamics itself has a type of error correction ability and can dynamically generate a classical linear code.