Measure and Forget Dynamics in Random Circuits

TL;DR

This paper explores how partial forgetting of measurement outcomes affects entanglement and thermalization in random Clifford circuits, revealing constant local thermalization rates and entropy behavior that challenge previous assumptions.

Contribution

It introduces the study of measurement-induced phase transitions with partial outcome forgetting, showing unique entropy dynamics and the disappearance of purification transitions.

Findings

Local thermalization rate remains constant regardless of system size

Entropy reaches a threshold and stops evolving as system size increases

Disappearance of the purification transition in the studied regime

Abstract

"Forgetful" measurements-physically similar to dephasing-are of interest both for applications to fault-tolerant quantum computing and fundamentally, in studying how entanglement and entropy spread. This paper investigates measurement-induced phase transitions (MIPT) in random Clifford circuits when measurement outcomes are partially forgotten. Our findings reveal a local thermalization rate that remains constant regardless of system size. We also numerically calculate the decay behavior at the turning points in the entropy diagram. We observe a counterintuitive phenomenon where the entropy reaches a threshold and stops evolving, even as the system size increases. This challenges an intuition, drawn from previous studies of noisy random circuits, that noise will cause the thermalization of the whole system. Additionally, we identify the disappearance of the purification transition and discuss the implications of these entanglement dynamics for quantum error-correction codes.