Scalable Probes of Measurement-Induced Criticality

We uncover a local order parameter for measurement-induced phase transitions: the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of measurement-induced criticality that are immediately applicable to advanced quantum computing platforms. We test our proposal on a 1+1 dimensional stabilizer circuit model that can be classically simulated in polynomial time. We introduce the concept of a "decoding light cone" to establish the local and efficiently measurable nature of this probe. We also estimate bulk and surface critical exponents for the transition. Developing scalable probes of measurement-induced criticality in more general models may be a useful application of noisy intermediate scale quantum devices, as well as point to more efficient realizations of fault-tolerant quantum computation.