Universal scaling and protocol-dependent amplitude in hybrid quantum walks

Abstract

Quantum walks spread ballistically but become diffusive with classical admixture. We compare two hybrid walks using identical quantum and classical steps at the same classical-step rate but ordered differently in time. Any nonzero admixture yields diffusion. Near the quantum limit, both diffusion coefficients have first-order poles, but their amplitudes differ by about a factor of two. The coherence timescale sets the pole order, while temporal organization sets the amplitude. We expect our analytical framework to apply broadly to quantum--classical hybrid systems.