Probabilistic representation of quantum dynamics

Il. I. Gikhman

Zbigniew Haba

Jincheng Zhang

This paper explores the integration of probabilistic matrix modeling with quantum computing to facilitate real-time system state modeling and prediction. Traditional probabilistic matrix approaches often struggle with dynamic environments, necessitating a novel dynamic adjustment mechanism. We introduce a framework that leverages quantum computing's inherent probabilistic properties to dynamically adjust matrix weights, enabling more accurate simulations and precise predictions. This work addresses the limitations of static parameter-based modeling by integrating quantum computation for enhanced system behavior representation. The core mechanism centers on adjusting probabilities based on quantum fluctuations, ultimately improving the responsiveness and accuracy of the modeling process. This represents a significant step towards adaptive system representation, particularly within complex, dynamic systems.

Hoang Vu

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.

Piotr Garbaczewski

Anatoli Polkovnikov