Critical properties of the measurement-induced transition in random quantum circuits

TL;DR

This paper investigates the measurement-induced phase transition in 1+1D Haar-random quantum circuits, estimating the critical measurement rate and critical exponents, revealing differences from stabilizer circuits and percolation, and providing insights into the transition's theoretical understanding.

Contribution

The study provides precise numerical estimates of the critical measurement rate and critical exponents for Haar-random circuits, highlighting differences from stabilizer circuits and percolation.

Findings

Critical measurement rate estimated at p_c = 0.17(1).

Critical exponents consistent with percolation and stabilizer circuits, but differ from previous Haar estimates.

Entanglement entropy prefactor varies with Re9nyi index n in Haar case.

Abstract

We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from that for stabilizer circuits or percolation, but we are unable to definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies $S_n$ depends strongly on the R\'enyi index $n$; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.