Emergence of drifted diffusion in quantum walks with subspace restart

This paper investigates how to control the quantum-to-classical crossover in discrete-time quantum walks (DTQWs). Traditional quantum walks exhibit ballistic spreading due to coherent interference, which is sensitive to environmental noise. The authors introduce a novel 'subspace restart' protocol that periodically resets only the internal coin degree of freedom while leaving the spatial probability distribution intact. By treating the system as a series of independent secondary sources, the authors employ a Huygens-Fresnel-type decomposition to analyze how this selective reset suppresses long-range correlations and forces the walker into a classical-like diffusive regime.

The authors demonstrate that subspace restart effectively engineers a drifted-diffusion process. In the high-frequency limit (resetting every step), the quantum walk reduces to a classical random walk where the drift velocity and diffusivity are determined by the initial coin state. For longer restart periods, the system maintains a 'classical backbone'—a Gaussian envelope of probability—while residual quantum interference survives only as short-range corrections within effective light cones. These corrections renormalize the transport coefficients without altering the fundamental linear-in-time scaling of the diffusion, providing a highly tunable mechanism for controlling transport in synthetic lattices.

This work provides a precise, tunable knob for bridging the gap between coherent quantum dynamics and classical stochastic transport. Unlike global resetting, which erases the system's history, subspace restart harnesses the walker's spatial memory to engineer specific transport properties. This approach is highly relevant for experimental quantum-walk platforms, such as photonic systems or time-multiplexed architectures, where active feed-forward control can be used to implement these selective resets.