Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits

TL;DR

This paper explores how measurements influence phase transitions in high-dimensional stabilizer circuits, revealing conformal transitions near percolation thresholds through extensive numerical analysis.

Contribution

It provides the first detailed characterization of measurement-induced phases and transitions in $(d+1)$-dimensional stabilizer circuits for $d=1,2,3$, highlighting their conformal nature.

Findings

Measurement-induced transition is conformal in $(d+1)$ dimensions.

Transitions are close to percolation thresholds in spatial dimensions.

Numerical simulations reveal entanglement and purification dynamics near criticality.

Abstract

The interplay between unitary dynamics and local quantum measurements results in unconventional non-unitary dynamical phases and transitions. In this paper we investigate the dynamics of $(d+1)$-dimensional hybrid stabilizer circuits, for $d=1,2,3$. We characterize the measurement-induced phases and their transitions using large-scale numerical simulations focusing on entanglement measures, purification dynamics, and wave-function structure. Our findings demonstrate the measurement-induced transition in $(d+1)$ spatiotemporal dimensions is conformal and close to the percolation transition in $(d+1)$ spatial dimensions.