Quantum Federated Learning

• Quantum Federated Learning is a paradigm that combines distributed, privacy-preserving federated learning with quantum computing to train quantum and hybrid models.
• It leverages quantum neural networks, secure aggregation protocols, and advanced optimizers like Quantum Natural Gradient Descent to address noise and data fragility.
• QFL demonstrates scalability and robustness in applications such as healthcare and IoT, overcoming challenges like quantum noise and hardware heterogeneity.

Quantum Federated Learning (QFL) is a paradigm that synergistically unites the distributed, privacy-preserving principles of federated learning (FL) with the computational capabilities of quantum machine learning (QML) and quantum networks. By orchestrating collaborative training of quantum or hybrid quantum-classical models across multiple clients—without the need to share raw local data—QFL addresses the dual challenges of quantum data fragility and privacy, while aiming to extend the scalability, efficiency, and security of distributed AI into the quantum regime (Nguyen et al., 21 Aug 2025, Mathur et al., 9 Apr 2025). QFL frameworks support purely quantum as well as hybrid classical–quantum settings, leverage both classical and quantum-secured communication protocols, and are optimized to account for quantum noise, heterogeneity of quantum hardware, and communication constraints.

1. Foundational Concepts and Taxonomy

QFL generalizes the federated learning concept to quantum settings, exploiting the computational advantages of superposition, entanglement, and quantum parallelism. Local clients—equipped with quantum processors (or, in hybrid models, with classical-quantum resources)—train quantum neural networks (QNNs), parameterized quantum circuits (PQCs), or variants such as quantum convolutional neural networks (QCNNs) on their private data (Chehimi et al., 2021, Nguyen et al., 21 Aug 2025). Only model updates or parameter shifts are exchanged, not raw data, native quantum states, or measurement results.

Major taxonomy axes include (Nguyen et al., 21 Aug 2025, Ren et al., 2023):

• Architecture: fully quantum (where all clients and aggregation steps are implemented with quantum processors, quantum channels, and direct quantum parameter sharing) vs. hybrid (where quantum models or optimizations are embedded within classical FL workflows, and classical–quantum model or measurement data are managed at different levels).
• Networking topology: centralized (single quantum server or aggregator), hierarchical (quantum edge aggregation before central aggregation), and decentralized (peer-to-peer quantum-secured update sharing, possibly via entanglement-based channels).
• Parameter encoding and update: classical communication of PQC parameter vectors, aggregation of density matrices, or (for fully quantum settings) transmission of quantum parameter states using quantum key distribution (QKD), teleportation, or entanglement-swapping schemes.

A detailed taxonomy also considers communication schemes (classical wireline/wireless vs. quantum links), quantum data encoding/decoding procedures, optimization algorithms (QNGD, QAOA, VQE), security primitives (QKD, quantum homomorphic encryption, quantum differential privacy), and application area (Nguyen et al., 21 Aug 2025, Ren et al., 2023).

2. Technical Architectures and Methodologies

QFL implementations universally include:

• Quantum local models: Variational quantum circuits (VQCs) or QNNs built with layers of parameterized unitary gates (often rotations and entangling gates such as CNOTs), accepting data encoded via amplitude or angle encoding (Qi et al., 2023, Liu et al., 22 Jan 2025).
• Local quantum training: Each client optimizes the circuit parameters using quantum-appropriate loss functions (e.g., fidelity, MSE, cross-entropy) and quantum-aware optimizers (e.g., quantum natural gradient descent, parameter shift rule).
• Quantum federated averaging: Analogous to classical FedAvg, quantum circuit parameters $\theta$ from all clients are aggregated (e.g., $\theta^{h+1}= \frac{1}{K}\sum_k \theta_k^h$), possibly using importance or Fisher-information weighting, quantization, or secure masking schemes (Liu et al., 22 Jan 2025, Bhatia et al., 23 Jul 2025).
• Privacy and security mechanisms: Secure multi-party aggregation is realized via QKD-based one-time pad masking and quantum secret sharing (Liu et al., 22 Jan 2025), quantum secure aggregation protocols, or quantum homomorphic encryption (Chu et al., 2023). When updates are encrypted, information-theoretic privacy is achieved and gradient inversion is provably prevented assuming honest-but-curious adversaries.
• Adaptations for scalability and robustness: Techniques include slimmable and multimodal quantum networks (where parameter subgroups can be separately communicated or fused via quantum entanglement layers) (Yun et al., 2022, Pokharel et al., 10 Jul 2025), as well as sporadic update mechanisms to suppress quantum noise-induced instability in NISQ devices (Rahman et al., 15 Jul 2025).

A typical communication/aggregation procedure involves client-side quantization and masking of the update vector, secure upload to the aggregator server, mod-$2^q$ summing of masked updates (with mask cancellation), and final dequantization to form the new global model (Liu et al., 22 Jan 2025).

3. Security, Privacy, and Communication Schemes

QFL fundamentally augments FL security through the intrinsic features of quantum communication:

• Quantum Key Distribution (QKD): QKD supplies symmetric keys for update masking and secure parameter aggregation, providing information-theoretic security that is resilient against both classical and quantum computational attacks (Liu et al., 22 Jan 2025, Ren et al., 2023).
• Quantum secure aggregation: Protocols leverage entangled GHZ states, modular secret sharing, and the Chinese Remainder Theorem for resistant multi-client sum computation without raw parameter disclosure (Yu et al., 2022).
• Quantum-enhanced differential privacy: Addition of quantum noise or randomization, or application of quantum cryptographic protocols, mitigates privacy leakage in both classical and quantum parameter update phases (Mathur et al., 9 Apr 2025).
• Quantum homomorphic encryption: Supports computation on encrypted quantum data, enabling servers to update global models without ever decrypting individual local contributions (Chu et al., 2023). In some protocols, ternary or cyclical quantization further reduces bandwidth and security exposure.
• Hybrid secure architectures: When quantum resources are limited, classical clients can interact with quantum servers via classical shadows (produced through shadow tomography), obtaining gradients by evaluating observables against server-produced shadow states (Song et al., 2023).

4. Optimization Algorithms and Noise Mitigation

Given the unique geometry and noise properties of quantum state manifolds, QFL integrates optimizations such as:

• Quantum Natural Gradient Descent (QNGD): Adjusts parameter update steps relative to the Fubini–Study metric, leveraging the underlying quantum state manifold for efficient convergence and reduced communication (Qi et al., 2023, Bhatia et al., 23 Jul 2025). The QNGD update is typically $$\theta_{t+1} = \theta_t - \eta (g^+(\theta_t) \nabla\mathcal{L}(\theta_t))$$, with $g^+$ being a pseudo-inverse of the metric tensor.
• Fisher Information-Based Aggregation: Aggregates client parameters by their local Fisher information magnitude, thus retaining parameters most sensitive to local data and enhancing robustness under non-IID conditions (Bhatia et al., 23 Jul 2025).
• Dynamic/slimmable model partitioning: Separates parameter sets (e.g., angle vs. pole parameters; submodel layers in slimmable/multimodal networks) for communication under time-varying channels; e.g., only essential pole parameters are transmitted when bandwidth is constrained (Yun et al., 2022).
• Sporadic/scheduled updating: Adaptive communication frequency or scaling masks contribution from clients with high quantum noise, improving convergence speed and reducing variance in gradient estimation (Rahman et al., 15 Jul 2025).
• Entanglement and quantum fusion: Intermediate or late fusion of outputs from multiple quantum circuits via entangling layers enables joint multimodal learning and robustness against missing or corrupted modalities (Pokharel et al., 10 Jul 2025).

5. Practical Implementations and Experimental Results

Recent QFL demonstrations include:

• Proof-of-concept quantum network deployment: Experimental realization of masked, key-distributed secure update aggregation on a four-client Sagnac quantum network; scaling simulations for 200+ clients with significant communication cost reduction by $75\%$ using 8– or 16–bit quantization (Liu et al., 22 Jan 2025).
• Algorithmic performance: Federated quantum models (e.g., using QNNs or QCNNs) on quantum data for cluster state classification, multipartite entanglement, and nonstabilizerness discrimination consistently outperform central or naive federated baselines, showing improved accuracy up to several percentage points with added quantum clients, and robust operation under both IID and non-IID data partitioning (Chehimi et al., 2021, Liu et al., 22 Jan 2025).
• Hybrids and classical clients: Simulation and deployment of frameworks (e.g., CC-QFL (Song et al., 2023), FedQNN (Innan et al., 16 Mar 2024), SlimQFL (Yun et al., 2022)) indicate scalability, resilience to system noise, and quantitative accuracy (often exceeding 86–90% on multi-class datasets) even on current NISQ-prevalent quantum hardware.
• Cloud-based and platform experiments: Many implementations utilize PennyLane (Xanadu), Qiskit (IBM), or combinations with TensorFlow Quantum/Federated or JAX-backends (Pokhrel et al., 1 May 2024, Nguyen et al., 21 Aug 2025). Preprocessing for efficient quantum encoding (especially amplitude encoding) is essential for large datasets on resource-limited quantum simulators or hardware.

6. Applications, Limitations, and Open Challenges

QFL frameworks are projected to have impact in:

• Healthcare and medical imaging: Secure, collaborative learning for privacy-critical institutions; e.g., ADNI (Alzheimer’s) dataset (Bhatia et al., 23 Jul 2025), ECG or biopsy data (Nguyen et al., 21 Aug 2025).
• Autonomous vehicular and satellite networks: Distributed anomaly detection, routing, and real-time collaborative inference using quantum federated averaging with on-device quantum accelerators (Nguyen et al., 21 Aug 2025).
• IoT, finance, and metaverse scenarios: Secure, scalable, and heterogeneous data fusion in constrained or privacy-sensitive deployments.
• Multimodal sensor networks: Cross-modal quantum processing for emotion recognition, smart cities, and complex cyber-physical systems (Pokharel et al., 10 Jul 2025).

Limitations and emerging research avenues include:

• System heterogeneity: Device-level diversity in qubit counts, noise rates, and connectivity requires adaptive aggregation, model partitioning, and standardization (Nguyen et al., 21 Aug 2025).
• Quantum noise and error resilience: Robust error mitigation, adaptive update scaling (e.g., SpoQFL (Rahman et al., 15 Jul 2025)), and integrated partial correction are necessary for realistic NISQ-era deployments.
• Communication constraints: Bandwidth and quantum channel fidelity in decentralized or quantum-enhanced topologies remain bottlenecks; optimization of aggregation intervals, quantization, and fusion strategies is ongoing (Sünkel et al., 15 Feb 2024).
• Standardization and benchmarking: Defining datasets, metrics, and protocol interfaces for cross-hardware and cross-algorithm interoperability (Nguyen et al., 21 Aug 2025).
• Integration with next-generation networks: Seamless co-design with 6G/quantum networks for ultra-low latency and high-security secure learning (Nguyen et al., 21 Aug 2025).
• Algorithmic robustness: Research is needed into extensions for adversarial robustness, quantum-aware differential privacy, and secure support for Byzantine/faulty clients (Mathur et al., 9 Apr 2025).

7. Summary Table of Notable QFL Architectures

Framework / Algorithm	Core Features	Key Contributions
QuNetQFL (Liu et al., 22 Jan 2025)	QKD-masked secure agg., quantization, NISQ/hybrid support	Experimental 4-client demo; scalability; privacy guarantees
QCNN-QFL (Chehimi et al., 2021)	Local QCNN on quantum data, hierarchical QFL dataset, TFQ+TFF integration	Realistic federated quantum data, robust with non-IID
QuantumFed (Xia et al., 2021)	Fidelity-maximizing unitary update, full quantum aggregation	Robust to noisy or incomplete local data
SlimQFL (Yun et al., 2022)	Separate pole/angle updating, dynamic upload under channel/energy constraints	Robust to harsh network, higher acc. under poor channels
eSQFL (Yun et al., 2022)	Depth-slmmable QNNs, inplace fidelity distillation, superposition coding	Channel-adaptive, mitigates entanglement entropy/barren plateaus
CryptoQFL (Chu et al., 2023)	QHE, QOTP, ternary quantization, optimized quantum adder	Privacy and computation efficient
SpoQFL (Rahman et al., 15 Jul 2025)	Noise-adaptive sporadic scaling, update skipping	Mitigates noise heterogeneity, higher stability
QFedFisher (Bhatia et al., 23 Jul 2025)	Fisher-based param. selection, layerwise adjustment	Improved performance, robustness to data heterogeneity
Multimodal QFL (Pokharel et al., 10 Jul 2025)	Entanglement-based intermediate fusion, missing modality agnostic (MMA)	Multimodal/heterogeneous data support, robust to missingness
CC-QFL (Song et al., 2023)	Classical clients, shadow tomography for gradient calculation	Quantum learning with only server-side quantum resources
General hybrid/benchmark (Nguyen et al., 21 Aug 2025, Mathur et al., 9 Apr 2025)	Comprehensive architecture taxonomy, end-to-end evaluation, open challenges	Integration roadmap, state-of-art summary

In sum, Quantum Federated Learning has emerged as a multidisciplinary research direction that incorporates foundational quantum information science, distributed optimization, and secure multiparty computation to address the scalability, security, and practical deployment of quantum-enhanced models in real-world, distributed environments. With continuing progress in quantum hardware, quantum network infrastructure, and quantum-specific machine learning algorithms, QFL is positioned as a central architectural paradigm for next-generation privacy-preserving AI.