Scalable probes of measurement-induced phase transitions

Measurement-induced phase transitions are a recently uncovered class of critical phenomena that occur when many-body unitary dynamics are interspersed with measurements at a tunable rate. We uncover a local order parameter for such measurement-induced criticality (MIC) equal to the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of MIC 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 determine bulk and surface critical exponents of MIC for such models and find that they are very close, or equal to those of 2+0-dimensional critical percolation. Developing scalable probes of MIC in more general models may be a useful application of noisy-intermediate scale quantum (NISQ) devices, as well as point to more efficient realizations of fault-tolerant quantum computation.