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arXiv:2410.08252

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

Michal Koren, Or Peretz

Published Oct 10, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2410.08252

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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.
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This paper introduces the ANMQ, a novel quantum algorithm leveraging adaptive matrix operations to enhance the efficiency of large-scale matrix computations. Traditional quantum algorithms often employ static complexity, limiting performance in scenarios requiring high throughput. ANMQ dynamically adjusts the computational complexity of matrix operations, enabling efficient processing of massive datasets. The core mechanism involves integrating quantum algorithms with adaptive matrix operations, allowing for a flexible and optimized computation strategy. This approach addresses the challenges associated with scaling quantum computation to large matrices, offering a potentially transformative advancement in quantum algorithm design. The paper details the algorithm's architecture, demonstrates its efficacy through theoretical analysis and preliminary simulations, and explores potential applications across various quantum computing domains.
Cloud computing has become an integral part of modern information technology infrastructure, providing scalability and flexibility to meet the demands of various applications. However, ensuring high availability and fault tolerance in cloud services is crucial for maintaining uninterrupted operations. Load balancing plays a vital role in distributing traffic efficiently across multiple servers to avoid overload and minimize service disruptions. Existing load balancing techniques require help to adapt to dynamic workloads, making them less reliable in cloud environments. Quantum computing handles complex optimization problems and offers a promising avenue for enhancing load balancing in the cloud. This research explores the concept of Fault-Tolerant Load Balancing (FTLB) in cloud computing with the integration of quantum computing. It investigates how quantum algorithms can optimize load-balancing decisions in real-time, considering dynamic workloads and server failures– the proposed novel quantum-load balancing (NQ-LB) algorithm designed to improve fault tolerance and resource utilization. The study employs a comparative analysis, evaluating the performance of the quantum-inspired load-balancing approach against classical load-balancing methods. We consider factors such as response time, resource allocation, fault tolerance, and scalability in a cloud computing environment. The results reveal the potential benefits of quantum computing in achieving fault-tolerant load balancing, particularly in scenarios with rapidly changing workloads and server failures. This research contributes to the advancement of cloud computing by harnessing the capabilities of quantum computing to enhance fault tolerance and load balancing. The findings can have implications for industries that rely on highly available cloud services, offering a more resilient infrastructure for critical applications.