Measurement-induced purification transition in a numerical free-fermion model

Quantum hybrid dynamics, involving unitary gates and projective measurements, have been shown in a wide array of cases to exhibit a measurement-induced purification transition. The “mixed” phases of such models take exponentially long to purify, and often have quantum error-correcting properties. We numerically study a case of hybrid dynamics in a specific fermion model. Motivated by a mapping to a statistical mechanics model, we study evolution by free-fermion gaussian unitary gates interspersed with projective measurements, and find evidence of such a phase transition. We plot the phase diagram, extract critical exponents for the transition, and compare the results to related models.