Quantum simulation of single-server Markovian queues: a dynamic amplification approach

Quantum computing is revolutionizing various fields, including operations research and queueing theory. This work presents a transformative quantum simulation framework that addresses the long-standing challenge of accurately modeling single-server Markovian queues, a fundamental problem in both quantum computing and stochastic modeling. Our approach introduces a dynamic amplitude amplification technique that leverages custom parameterized quantum gates to model Poisson arrivals and exponential service times in real time. The core innovation lies in the adaptive adjustment of these gate parameters, which selectively amplifies critical quantum states based on evolving queue conditions. This dynamic mechanism not only accelerates convergence towards theoretical predictions but also significantly reduces computational overhead compared to static quantum methods. Empirical evaluations demonstrate accuracy across diverse traffic scenarios, with relative errors dropping below 0.002 in high-traffic regimes. By effectively bridging the gap between classical queueing theory and quantum simulation, our method opens new avenues for leveraging quantum resources to tackle complex stochastic processes in operations research.