Year: 2026
Type: preprint
Abstract: We study the geometric spread of discrete-time quantum walks using Connes' distance formula. We introduce its discrete analogue by adapting the continuous spectral metric to the lattice, with the Dirac operator replaced by the unitary step operator. Focusing first on a (2+1)-dimensional quantum walk, we evaluate the dynamical spread of localized wavepackets to compare propagation in free space against that under a uniform magnetic field. We find that while the free walk shows linear ballistic growth, gauge-induced phases in the magnetic walk constrain the admissible test operators, suppressing the long-time geometric expansion. Furthermore, we apply this discrete framework to a (1+1)-dimensional plastic quantum walk simulating an inhomogeneous spatial metric. The results demonstrate that the discrete Connes distance naturally captures the underlying spatially varying metric, providing a robust measure of the wavepacket's spread that adapts directly to the local simulated geometry.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1693829329, Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés, Initiative Nationale Hybride HPC Quantique - Acquisition, Taming Quantum Causality, WithOut SpaceTime (WOST), G7080048889
OpenAlex ID: W7214671112