Entanglement Steering in Adaptive Circuits with Feedback

TL;DR

This paper introduces adaptive quantum circuits with feedback that show entanglement phase transitions both at the trajectory level and in the averaged density matrix, revealing different critical points and universality classes.

Contribution

It presents a novel class of feedback-based adaptive circuits exhibiting distinct entanglement transitions at different measurement thresholds.

Findings

Density matrix transition belongs to the parity-conserving universality class.

Entanglement transition in individual trajectories occurs at a different measurement rate.

Feedback steers the density matrix towards a unique state above a threshold.

Abstract

The intensely studied measurement-induced entanglement phase transition has become a hallmark of non-unitary quantum many-body dynamics. Usually, such a transition only shows up at the level of each individual quantum trajectory, and is absent for the density matrix averaged over measurement outcomes. In this work, we introduce a class of adaptive random circuit models with feedback that exhibit transitions in both settings. After each measurement, a unitary operation is either applied or not depending on the measurement outcome, which steers the averaged density matrix towards a unique state above a certain measurement threshold. Interestingly, the transition for the density matrix and the entanglement transition in the individual quantum trajectory in general happen at \textit{different} critical measurement rates. We demonstrate that the former transition belongs to the parity-conserving universality class by an explicit mapping to a classical branching-annihilating random walk process.