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Applied Sciences

Quantum Deep Q-Network for Intelligent Packet Routing in 6G Heterogeneous Wireless Networks

Tong Xie, Taoyong Li, Xinxin Yuan, Jiacheng Ni

Published Jun 16, 2026• 1 citation
Publisher

Abstract

Intelligent packet routing in sixth-generation (6G) heterogeneous wireless networks must contend with stochastic link failures, heterogeneous delay profiles, and the severe memory constraints of edge nodes. We propose a quantum deep Q-network (Q-DQN) that replaces the multi-layer perceptron in a standard DQN agent with a six-qubit variational quantum circuit (VQC) employing ring-topology entanglement and angle embedding. The total trainable parameter count follows the closed-form expression |ϕ|=12L+7n, growing at only seven parameters per additional network node. On a 10-node heterogeneous topology with stochastic link failures, Q-DQN achieves an average end-to-end delay of 54.29±1.72 ms with only 106 parameters, a 49.6× reduction relative to the MLP-based DQN baseline (5258 parameters, 52.89±2.67 ms). A three-seed scalability evaluation across n∈{6,8,10,12} nodes shows that under a limited 200-episode training budget DQN converges more consistently, while Q-DQN matches DQN performance under full 500-episode training at a fraction of the parameter cost. Ablation experiments confirm that local-topology entanglement substantially outperforms full-connection alternatives. These results indicate that VQC-based routing agents can match classical counterparts at a fraction of the parameter cost, providing a path toward ultra-lightweight intelligent routing in 6G edge deployments.

DOI
10.3390/app16126096

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Intelligent packet routing in sixth-generation (6G) heterogeneous wireless networks must contend with stochastic link failures, heterogeneous delay profiles, and the severe memory constraints of edge nodes. We propose a quantum deep Q-network (Q-DQN) that replaces the multi-layer perceptron in a standard DQN agent with a six-qubit variational quantum circuit (VQC) employing ring-topology entanglement and angle embedding. The total trainable parameter count follows the closed-form expression |ϕ|=12L+7n, growing at only seven parameters per additional network node. On a 10-node heterogeneous topology with stochastic link failures, Q-DQN achieves an average end-to-end delay of 54.29±1.72 ms with only 106 parameters, a 49.6× reduction relative to the MLP-based DQN baseline (5258 parameters, 52.89±2.67 ms). A three-seed scalability evaluation across n∈{6,8,10,12} nodes shows that under a limited 200-episode training budget DQN converges more consistently, while Q-DQN matches DQN performance under full 500-episode training at a fraction of the parameter cost. Ablation experiments confirm that local-topology entanglement substantially outperforms full-connection alternatives. These results indicate that VQC-based routing agents can match classical counterparts at a fraction of the parameter cost, providing a path toward ultra-lightweight intelligent routing in 6G edge deployments.
The recent convergence of 6G wireless systems and Tiny Machine Learning (TinyML) has driven the need for on-device intelligence in edge networks, where ultra-low latency, stringent energy budgets, and tight compute constraints demand novel architectures. Lightweight deep models efficiently extract local patterns but fail to capture global dependencies, while attention mechanisms do so at the expense of energy and computational cost. To bridge this gap, we introduce Quantumer, a hybrid TinyML--quantum framework that integrates multi-scale dilated convolutions and scaled dot-product attention within a lightweight transformer architecture, employing a two-stage transfer learning pipeline from Quantum Pre-Training (Quantumer-Q) to Classical Fine-Tuning (Quantumer-C). We also present QuantiblentLayer, a four-qubit variational circuit that maps compact traffic representations into measurement-based Hilbert-space features using trainable rotations and cyclic entangling operations. The circuit is used only during offline pre-training as a nonlinear embedding teacher and is removed before Quantumer-C deployment, leaving a fully classical inference model without runtime quantum execution. By transferring these quantum-assisted embeddings into an energy-efficient, lightweight transformer, Quantumer achieves strong detection performance with minimal compute and memory overhead on resource-constrained edge devices. The intrusion detection system (IDS) is used as a case study and evaluated on the Edge-IIoTset, TON IoT, and WUSTL-IIoT-2021 datasets. Quantumer-Q achieves competitive compact-model performance with 105.86K parameters, 0.4038 MB memory usage, 0.5525 MB model size, and 5.5646 MFLOPs; the INT8 Raspberry Pi 4 deployment obtains 16.8413 ms latency with a 0.6493 MB footprint. These results support training-time quantum-assisted representation learning for compact edge-deployable IDS.
The impending transition to sixth-generation (6G) wireless networks introduces the operational deployment of sub-terahertz and terahertz (sub-THz/THz) frequency bands (0.1 THz to 1.0 THz, specifically the 140 GHz D-Band and 300 GHz transmission windows) to support multi-terabit-per-second (Tbps) data rates and sub-0.1 millisecond Ultra-Reliable Low-Latency Communication (URLLC). However, the physics of THz electromagnetic propagation—characterized by severe atmospheric molecular absorption, extreme free-space path loss, and shadow attenuation from dynamic blockages—demands narrow pencil-beam hybrid beamforming alongside massive Reconfigurable Intelligent Surfaces (RIS). When millions of autonomous vehicles, aerial drones, and mobile devices traverse high-density urban environments, joint real-time spectrum sub-band scheduling, continuous phase-shift tracking, and power allocation induce an NP-hard combinatorial optimization problem scaling exponentially as O(K^N). Classical Deep Reinforcement Learning (DRL) frameworks, such as Deep Q-Networks (DQN) and Soft Actor-Critic (SAC) executing on high-performance host GPUs, suffer from a prohibitive computational inference barrier (requiring 28.5 ms to 74.2 ms per scheduling decision), fundamentally violating the 6G URLLC scheduling budget (<1.0 ms). This paper proposes and rigorously evaluates a Parameterized Variational Quantum Reinforcement Learning (VQRL) framework utilizing quantum state amplitude-phase embedding and parameterized rotation-entanglement quantum circuits (VQC) executed on superconducting NISQ quantum co-processors. By evaluating multi-user allocation policies simultaneously in quantum superposition across a 2^N-dimensional Hilbert space and eliminating multi-cell co-channel interference through inter-tower quantum entanglement, VQRL achieves: • Exponential Latency Reduction: Slashes scheduling execution latency to just 0.078 milliseconds (78 microseconds)—a 365x speedup over GPU-based DQN—comfortably meeting 6G sub-millisecond sub-frame budgets.• Superior Convergence Speed: Achieves a 94.2% reduction in training convergence time (converging within 42 episodes versus 720 episodes for double DQN).• Massive Multi-Terabit Throughput: Delivers an aggregate cell throughput of 1.48 Tbps (a 2.84x improvement over classical DQN baselines) under 3GPP Urban Microcell (UMi) topographies.• High-Mobility Vehicular Beam Tracking: Eliminates 98.6% of vehicular beam-alignment dropouts under 120 km/h mobility through predictive quantum Hamiltonian evolution.• Energy Efficiency: Reduces base station computational energy consumption from 480 Watts to 24 Watts per radio frame. The repository includes the full 31-page primary academic treatise, complete novelty and systems defense dossiers, and full Hindi and Marathi translations.
The quantum machine learning (QML) paradigms and their synergies with network slicing can be envisioned to be a disruptive technology on the cusp of entering to era of sixth-generation (6G), where the mobile communication systems are underpinned in the form of advanced tenancy-based digital use-cases to meet different service requirements. To overcome the challenges of massive slices such as handling the increased dynamism, heterogeneity, amount of data, extended training time, and variety of security levels for slice instances, the power of quantum computing pursuing a distributed computation and learning can be deemed as a promising prerequisite. In this intent, we propose a cloud-native federated learning framework based on quantum deep reinforcement learning (QDRL) where distributed decision agents deployed as micro-services at the edge and cloud through Kubernetes infrastructure then are connected dynamically to the radio access network (RAN). Specifically, the decision agents leverage the remold of classical deep reinforcement learning (DRL) algorithm into variational quantum circuits (VQCs) to obtain the optimal cooperative control on slice resources. The initial numerical results show that the proposed federated QDRL (FQDRL) scheme provides comparable performance than benchmark solutions and reveals the quantum advantage in parameter reduction. To the best of our knowledge, this is the first exploratory study considering an FQDRL approach for 6G communication network.
Quantum routing is crucial for future networks as it utilizes entanglement and swapping to establish efficient communication paths between nodes. Although machine learning has transformed various industries, its integration with quantum networking remains relatively underexplored. To address this gap, we present the Deep Quantum Routing Agent (DQRA), an innovative deep reinforcement learning framework that optimizes routing paths to maximize request fulfillment within constrained time windows. Our approach integrates a neural network with a qubit-preserving shortest-path algorithm, employing a reward-based training system to enhance connection success rates. Extensive experiments show DQRA achieves over 80% routing success in resource-limited networks and maintains approximately 60% effectiveness under challenging single-repeater conditions. Importantly, the model demonstrates polynomial-time complexity, ensuring scalable deployment and effectively merging machine learning with quantum network optimization
The vehicle routing problem (VRP) is a fundamental NP-hard task in intelligent transportation systems with broad applications in logistics and distribution. Deep reinforcement learning (DRL) with Graph Neural Networks (GNNs) has shown promise, yet classical models rely on large multi-layer perceptrons (MLPs) that are parameter-heavy and memory-bound. We propose a Quantum Graph Attention Network (Q-GAT) within a DRL framework, where parameterized quantum circuits (PQCs) replace conventional MLPs at critical readout stages. The hybrid model maintains the expressive capacity of graph attention encoders while reducing trainable parameters by more than 50%. Using proximal policy optimization (PPO) with greedy and stochastic decoding, experiments on VRP benchmarks show that Q-GAT achieves faster convergence and reduces routing cost by about 5% compared with classical GAT baselines. These results demonstrate the potential of PQC-enhanced GNNs as compact and effective solvers for large-scale routing and logistics optimization.
Abstract The innovative dynamics of communication networks are being challenged unprecedentedly by rising data traffic, dynamically evolving topologies, and the increased complexity of distributed intelligent applications. Typically, routing algorithms are inadequate for adjusting in actual time to address network congestion, changes in computational needs and heterogeneity and real-time. In this paper, we propose a new hybrid quantum-augmented routing model that synergistically integrates quantum reinforcement learning with physics-motivated network modeling by reasoning in terms of a space‒time continuum. Here, the phenomenon of network congestion is simulated as a curvature on the fabric of space-time, and the computation facilities on nodes are envisioned as a gravitational source, which directs the flows of data. The most essential innovation is the development of an artificial intelligence awareness layer (AIAL), that functions with quantum-aid learning agents proactively weighing and choosing the routing paths in live environments. The quantum agents query the multiple parallel paths in SQL via quantum superposition and quantum parallelism to enhance convergence and global route optimization. The hybrid structure is built upon features of the local adaptability of quantum-enhanced Q-learning and global contextual knowledge of deep Q-networks (DQNs), which are constantly adjusted to changes in network metrics, such as the load, latency, and availability of nodes. Large simulations demonstrate that this structure has a reward/cost ratio of 138.16, scales well during states of extreme congestion and is structurally efficient in all cases, with higher resiliency and faster convergence of the framework than those of OSPF, the EIGRP, the IS-IS and the RIP. Although this is a positive finding, it is reached under certain simulation conditions and it is not directly applicable in real-life network with diverse topologies and traffic patterns. The findings corroborate that coupling quantum reinforcement learning with physics-inspired routing will make full use of the adaptive optimal routing discoverable in uncertain situations, changing network conditions in an autonomous manner. This study establishes a basis for a new generation of cognitively adaptive, self-optimizing networks to best meet the needs of 6G, edge computing and quantum-aware distributed infrastructures.