Unveiling a Hidden Percolation Transition in Monitored Clifford Circuits: Inroads from ZX-Calculus

TL;DR

This paper reveals that the measurement-induced phase transition in Clifford circuits, previously thought to be distinct from classical percolation, is actually governed by an underlying percolation transition uncovered through ZX-calculus analysis.

Contribution

The authors demonstrate that ZX-calculus techniques can uncover a hidden percolation transition underlying the MPT in Clifford circuits, linking quantum and classical critical phenomena.

Findings

ZX-calculus reveals a hidden percolation transition

Classical percolation coincides with the MPT in simplified networks

MPT is controlled by a classical percolation transition in disguise

Abstract

We revisit the measurement-induced phase transition (MPT) in Clifford circuits, which are both classically simulable and exhibit critical behavior widely believed to be distinct from classical percolation theory, using ZX-calculus. We analyze the MPT in a dynamical model composed of CNOT, SWAP, identity gates, and Bell-pair measurements, respectively, arranged randomly in a brickwork pattern. Our circuits exhibit a transition that is seemingly distinct from classical percolation based on standard arguments, that is in line with the prevailing understanding in the field. In contrast, by employing ZX-calculus based simplification techniques, we unveil a hidden percolation transition within the circuit structure. Over a range of parameters tied to the probabilities for applying different gates, we demonstrate that the classical percolation transition in the ZX-simplified network coincides with the MPT observed through mutual information. Our findings suggest that the MPT in Clifford circuits is, in fact, controlled by a classical percolation transition in disguise.