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

Quantum computing is revolutionizing various fields, including operations research and queueing theory. This study presents a quantum method for simulating single-server Markovian (M/M/1) queues, making quantum computing more accessible to researchers in operations research. We introduce a dynamic amplification approach that adapts to queue traffic, potentially improving simulation efficiency, and design custom-parameterized quantum gates for arrival and service processes. This flexible framework enables modeling of various queueing scenarios while bridging quantum computing and classical queueing theory. Notably, our quantum method shows potential advantages over classical simulations, particularly in high-traffic scenarios. This quantum simulation approach opens new possibilities for analyzing complex queueing systems, potentially outperforming classical methods in challenging scenarios and paving the way for quantum-enhanced operations research. The method was implemented and tested across low-, moderate-, and high-traffic scenarios, comparing quantum simulations with both theoretical formulas and classical simulations. Results demonstrate high agreement between quantum computations and theoretical predictions, with relative errors below 0.002 for effective arrival rates in high-traffic scenarios. As the number of qubits increases, we observe rapid convergence to theoretical values, with relative errors decreasing by up to two orders of magnitude in some cases. Sensitivity analysis reveals optimal parameter regions yielding errors lower than 0.001.