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

Hoang Vu

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arXiv · 2607.23569

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

Hoang Vu

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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.

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Hoang Vu. 2026-07-26. A Probabilistic Representation for Multi-State Discrete-time Quantum Walks. https://arxiv.org/abs/2607.23569

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