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Feynman Formula for Discrete-Time Quantum Walks
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DOI：10.1007/s10955-026-03619-w.png)
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Abstract
En 中文
We explicitly connect (discrete-time) quantum walks on 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.
Keywords:
Quantum walks
Markov additive process
Feynman Formula
Quantum transport PDEs
Journal
J
IF:
1.2
Papers:
106
Citations:
1.0W
