Measurement-induced criticality as a data-structure transition

TL;DR

This paper uses unsupervised learning methods to detect a measurement-induced phase transition in quantum systems, revealing new order parameters directly from raw data, and pioneering their application in dynamical quantum phase transitions.

Contribution

It introduces the use of principal component analysis and intrinsic dimension estimation to identify phase transitions in quantum data without prior labeling.

Findings

Identified a measurement-induced structural transition in quantum data space.

Defined novel order parameters directly from raw data.

Demonstrated the effectiveness of unsupervised tools in dynamical quantum phase transitions.

Abstract

We employ unsupervised learning tools to identify different phases and their transition in quantum systems subject to the combined action of unitary evolution and stochastic measurements. Specifically, we consider principal component analysis and intrinsic dimension estimation to reveal a measurement-induced structural transition in the data space. We test our approach on a 1+1D stabilizer circuit and find the quantities of interest furnish novel order parameters defined directly in the raw data space. Our results provide a first use of unsupervised tools in dynamical quantum phase transitions.