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

• URL: http://arxiv.org/abs/2607.23569v1
• Date: Sun, 26 Jul 2026 09:41:26 GMT
• Title: A Probabilistic Representation for Multi-State Discrete-time Quantum Walks
• Abstract summary: Building upon the pioneering framework of Vu (2026), we construct a probabilistic representation for three-state discrete-time quantum walks on integer lattices.<n>We establish that this representation converges to the continuum solution of multi-state Dirac partial differential equations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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