Many-Body-Localization Transition in a Universal Quantum Circuit Model

We develop both exact and approximate methods to compute out-of-time-ordered correlators for arbitrary universal quantum circuits, taking advantage of the mapping of quantum circuits to the dynamics of interacting fermions in one dimension. In this framework, the out-of-time-ordered correlator can be calculated exactly as a superposition of exponentially many Gaussian-fermionic trajectories in the number of interaction gates. We develop a variationally-optimized, Gaussian approximation to the spatial propagation of an initially-local operator by restriction to the fastest-traveling fermionic modes, in a similar spirit as light-front computational methods in quantum field theory. We demonstrate that our method can detect the many-body localization transitions of generally time-dependent dynamics without the need for perturbatively weak interactions.