Many-Body-Localization Transition in Matchgate-Dominated Quantum Circuits

We demonstrate the application of new technical tools for characterizing the many-body-localization transition in quantum circuits. Namely, we examine the behavior of the out-of-time-ordered (OTO) correlator, a four-point correlation function between two local observables, one of which is time-evolved. We are able to extend the number of qubits for which this quantity may be classically evaluated efficiently by decomposing universal quantum circuits into matchgate circuits, which describe free-fermion evolution, together with non-matchgates describing fermion interactions. For circuits composed only of matchgates, there exists a simulation technique for the OTO correlator which scales efficiently in the number of qubits, and exponentially with the number of interaction gates when extended to computational universality. Nevertheless, we find that for sufficiently weak interactions, this quantity may be efficiently approximated using perturbation theory. This allows us to numerically characterize the many-body localization transition in a regime which has so-far remained unexplored.