Feynman Formula for Discrete-time Quantum Walks
Probability
2025-10-16 v2 Mathematical Physics
math.MP
Abstract
We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs in continuous time and space with a phase interaction term. Our probabilistic representation for this type of PDE offers an efficient Monte Carlo computational technique.
Cite
@article{arxiv.2510.12038,
title = {Feynman Formula for Discrete-time Quantum Walks},
author = {Jean-Pierre Fouque and Tomoyuki Ichiba and Ka Lok Lam},
journal= {arXiv preprint arXiv:2510.12038},
year = {2025}
}
Comments
3 Figures, 33 pages