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Quantum Engineering

Performance analysis of quantum channels

Fengyou Sun

Published Mar 13, 2020• 19 citations
Publisher

Abstract

We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, and for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, that is, backlog, delay, and throughput.

DOI
10.1002/que2.35

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We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, and for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, that is, backlog, delay, and throughput.
We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, i.e., backlog, delay, and throughput.
We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, i.e., backlog, delay, and throughput.
The convergence of quantum computing and classical service system modeling presents a transformative opportunity. This paper proposes the formalization of Quantum Queueing Theory (QQT), a novel framework for modeling, analyzing, and optimizing service systems where quantum processors act as servers, quantum algorithms constitute service tasks, and quantum communication channels facilitate arrivals and departures. We outline the fundamental challenges posed by quantum mechanics (superposition, entanglement, measurement, decoherence) to classical queueing paradigms. Key research directions include defining quantum analogues of arrival processes, service disciplines, and performance metrics (quantum fidelity, task success probability, decoherence-limited waiting time). We explore modeling approaches leveraging quantum stochastic processes, quantum walks, and modified Lindblad master equations. The paper details critical areas for future research: hybrid quantum-classical queueing networks, resource allocation under decoherence, stability analysis in the quantum regime, and the development of quantum-aware scheduling policies. QQT is poised to become essential for designing efficient and scalable quantum computing data centers, quantum cloud services, and integrated quantum-classical computing infrastructures.
We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum `queue-channel.' Focusing on quantum erasures, we obtain an explicit single-letter capacity formula in terms of the stationary waiting time of qubits in the queue. Our capacity proof also implies that a `classical' coding/decoding strategy is optimal, i.e., an encoder which uses only orthogonal product states, and a decoder which measures in a fixed product basis, are sufficient to achieve the classical capacity of the quantum erasure queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.
We present a queueing model for a quantum communication network consisting of a primary queue and a service queue in which Bell pairs are formed and stored. The Bell pairs are inherently extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system via a stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue.
We consider a setting where qubits are processed sequentially, and derive fundamental limits on the rate at which classical information can be transmitted using quantum states that decohere in time. Specifically, we model the sequential processing of qubits using a single server queue, and derive explicit expressions for the capacity of such a `queue-channel.' We also demonstrate a sweet-spot phenomenon with respect to the arrival rate to the queue, i.e., we show that there exists a value of the arrival rate of the qubits at which the rate of information transmission (in bits/sec) through the queue-channel is maximized. Next, we consider a setting where the average rate of processing qubits is fixed, and show that the capacity of the queue-channel is maximized when the processing time is deterministic. We also discuss design implications of these results on quantum information processing systems.