Southwest Quantum Information and Technology

Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable propagation in time-dependent disorder

Presenting Author: Adrian Chapman, CQuIC, New Mexico
Contributing Author(s): Akimasa Miyake

Matchgate circuits have been extensively studied due to (i) their classical simulability properties and (ii) their close connection to the physics of noninteracting fermions in one dimension. We extend (i) by introducing a classically efficient algorithm for the Lieb-Robinson commutator norm of a local observable under Heisenberg evolution by a nearest-neighbor matchgate circuit. This is surprising in light of the fact that the Heisenberg evolution itself cannot even be stored efficiently by a classical computer in general. We apply our result by (ii) to the study of fermions propagating through a one-dimensional lattice in the presence of spatio-temporally fluctuating disorder and demonstrate a method to classify this propagation into either the localized, diffusive, or ballistic dynamical phase. We find that our results coincide with known classifications of Anderson localization in the statically disordered case, but the localized phase can also be seen to survive in the presence of weakly fluctuating disorder. We expect our results to inspire the application of localization as a classical simulation technique for more general classes of quantum circuits.

(Session 12 : Saturday from 2:15pm - 2:45pm)