A Probabilistic Representation for Multi-State Discrete-time Quantum Walks

Abstract:Building upon the pioneering framework of Vu (2026), we construct a probabilistic representation for three-state discrete-time quantum walks on integer lattices and validate it through empirical examples. Furthermore, we establish that this representation converges to the continuum solution of multi-state Dirac partial differential equations. Broadly, our findings demonstrate that this probabilistic paradigm serves as a robust alternative for simulating higher-dimensional quantum walks, opening new theoretical avenues to analyze quantum dynamics using classical stochastic processes.

arXiv:2607.23569 [quant-ph]

(or arXiv:2607.23569v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.23569 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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