Measurement-induced criticality as a data-structure transition

Understand

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.