Feynman Formula for Discrete-Time Quantum Walks
Abstract
Abstract We explicitly connect (discrete-time) quantum walks on $$\mathbb {Z} $$ Z with a four-state Markov additive process via a Feynman-type formula (13). 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.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Publication details
- Journal / source
- Journal of Statistical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 193
- Issue
- 5
- Publication date
- 9 May 2026
- Language
- EN