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AdeptHEQ-FL: Adaptive Homomorphic Encryption for Federated Learning of Hybrid Classical-Quantum Models with Dynamic Layer Sparing

AdeptHEQ-FL is a unified hybrid classical-quantum federated learning framework that integrates adaptive homomorphic encryption, dynamic layer sparing, and accuracy-weighted aggregation to simultaneously enhance model performance, ensure formal privacy guarantees, and minimize communication overhead in non-IID decentralized environments.

Original authors: Md Abrar Jahin, Taufikur Rahman Fuad, M. F. Mridha, Nafiz Fahad, Md. Jakir Hossen

Published 2026-05-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Md Abrar Jahin, Taufikur Rahman Fuad, M. F. Mridha, Nafiz Fahad, Md. Jakir Hossen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a group of friends trying to solve a giant jigsaw puzzle together, but with a few strict rules:

No one can show their puzzle pieces to anyone else (Privacy).
Everyone has a different mix of pieces (Non-IID data).
They can only send tiny text messages to share progress (Communication limits).
They want to use a special "quantum" tool that makes the puzzle-solving super powerful, but it's fragile and hard to use (Quantum Models).

This paper introduces AdeptHEQ-FL, a new system designed to help these friends solve the puzzle faster, more accurately, and more securely than ever before. Here is how it works, broken down into simple parts:

1. The Hybrid Team (Classical + Quantum)

Most puzzle-solving teams use standard tools (Classical AI). This paper suggests a "hybrid" team.

The Classical Part (The CNN): Think of this as the team's eyes. It looks at the raw images (like a photo of a cat or a car) and breaks them down into basic shapes and textures. It's good at the "heavy lifting" of seeing patterns.
The Quantum Part (The PQC): Think of this as the team's "super-brain." Once the eyes have done their job, the super-brain takes over. It uses Quantum Circuits to find complex, hidden connections between the pieces that a normal brain might miss.
The Result: By combining the steady eyes of the classical computer with the super-brain of the quantum computer, the team can solve harder puzzles (like the complex CIFAR-10 dataset) much better than teams using just one or the other.

2. The "Smart Vote" System (Adaptive Aggregation)

In a normal group project, everyone's opinion counts the same. But in this paper, the system realizes that some friends are doing a better job than others.

The Problem: If a friend is struggling (because their puzzle pieces are weird or incomplete), their bad advice shouldn't drag the whole group down.
The Solution: The system checks how well each friend is doing on a practice test. However, to protect their privacy, it adds a little bit of "static noise" to the score (Differential Privacy) so no one knows the exact score of anyone else.
The Vote: The system then gives a bigger vote to the friends with the higher (noisy) scores and a smaller vote to those struggling. This ensures the final model is built on the best ideas, even if the data is messy.

3. The "Secret Envelope" (Selective Encryption)

Usually, keeping secrets in a group chat is expensive and slow. If you encrypt everything, the messages become huge and take forever to send.

The Innovation: Instead of putting the entire puzzle solution in a heavy, locked safe (Full Encryption), the system only locks the most critical part of the solution: the final layer that decides what the picture actually is.
The Analogy: Imagine sending a letter. You don't need to lock the whole envelope in a bank vault; you just need to put the final signature in a sealed, tamper-proof tube. This keeps the most sensitive part private without slowing down the whole process.

4. The "Freeze" Button (Dynamic Layer Sparing)

Sending updates back and forth takes time and data.

The Strategy: The system watches which parts of the puzzle are changing a lot and which parts have stopped changing.
The Action: If a part of the model (like the early layers that just look for edges) isn't changing much, the system says, "Freeze that part! Don't send updates for it." It saves bandwidth.
The Exception: The "Super-Brain" (the Quantum layers) is never frozen. It is allowed to keep learning and adapting because it is the most flexible and important part of the team.

What Did They Find?

The authors tested this system on three different "puzzles" (datasets): CIFAR-10 (complex images), SVHN (house numbers), and Fashion-MNIST (clothing).

The Winner: AdeptHEQ-FL beat the other methods. On the hardest puzzle (CIFAR-10), it was about 25% more accurate than a standard quantum team and 14% more accurate than a team that tried to encrypt everything.
Efficiency: By freezing the unimportant layers and only encrypting the final step, the system saved a lot of communication time and data.
Resource Usage: Interestingly, their "hybrid" team used fewer quantum resources (4 qubits) than the competitors (6 qubits) but still performed better. This proves that a smart strategy is more important than just having more raw power.

The Bottom Line

AdeptHEQ-FL is like a highly organized, privacy-focused study group. It uses a mix of standard and super-powered tools, listens more to the smartest members (without knowing exactly who they are), locks up only the most sensitive secrets, and stops wasting time updating parts of the plan that aren't changing. The result is a faster, more accurate, and more secure way for machines to learn together without sharing their private data.

Technical Summary of AdeptHEQ-FL: Adaptive Homomorphic Encryption for Federated Learning of Hybrid Classical-Quantum Models with Dynamic Layer Sparing

1. Problem Statement

Federated Learning (FL) faces a triad of interconnected challenges: statistical heterogeneity arising from non-Identical and non-Independently Distributed (non-IID) data, privacy vulnerabilities inherent in model updates despite data localization, and high communication/computational overheads. Existing solutions often address these issues in isolation. Quantum FL (QFL) frameworks improve model expressivity but frequently lack formal privacy guarantees or robustness to non-IID data. Conversely, privacy-preserving techniques like Differential Privacy (DP) and Homomorphic Encryption (HE) often degrade utility in non-IID settings or incur prohibitive computational costs. Furthermore, efficiency-focused methods typically neglect quantum capabilities. There is a critical gap for a unified framework that simultaneously optimizes performance, privacy, and efficiency within a hybrid classical-quantum context.

2. Methodology

The proposed framework, AdeptHEQ-FL, integrates four core components to address these gaps:

Hybrid CNN-PQC Architecture: The model combines a classical Convolutional Neural Network (CNN) for feature extraction with a Parameterized Quantum Circuit (PQC) for enhanced feature processing.
- Classical Component: A CNN with three sequential convolutional blocks (convolution, ReLU, max-pooling) followed by fully connected layers extracts localized features (edges, textures). The output is flattened into a vector $f_{CNN} \in \mathbb{R}^{2^n}$ .
- Quantum Component: The classical features are encoded into a 4-qubit quantum state via amplitude embedding. The PQC utilizes two layers of "Strongly Entangling Layers," comprising parameterized single-qubit rotations ( $R_z, R_y, R_z$ ) and Controlled-NOT (CNOT) entanglement gates. The circuit outputs a 4-dimensional quantum feature vector via Pauli-Z measurements, which is then mapped to the final classification output by a classical fully connected layer.
Adaptive Accuracy-Weighted Aggregation with Differential Privacy: To handle non-IID data, the server aggregates client updates based on their local validation performance.
- Clients privatize their validation accuracy using the Laplace mechanism to ensure $(\epsilon, 0)$ -Differential Privacy per round.
- The server computes aggregation weights using a numerically stable tempered softmax over these privatized accuracies. This prioritizes contributions from high-performing clients while maintaining robustness against noise.
Selective Homomorphic Encryption (HE): To ensure privacy without incurring the full overhead of Fully Homomorphic Encryption (FHE), the framework applies the CKKS scheme selectively. Only the parameters of the final fully connected layer (FC4) are encrypted during transmission and aggregation. Other layers are aggregated in plaintext. The server decrypts the aggregated FC4 layer using its secret key after weighted summation.
Dynamic Layer-Wise Adaptive Freezing: To minimize communication overhead, the framework employs a mechanism to freeze less impactful classical layers.
- Layer importance is scored based on the L2 norm of parameter changes across rounds, smoothed via an Exponential Moving Average (EMA).
- Layers with scores below a fixed threshold (0.001) are frozen (parameters are not updated or transmitted).
- Crucially, quantum layers are explicitly exempted from freezing to preserve their adaptability and expressivity, which are vital for modeling complex patterns in decentralized data.

3. Key Contributions

The paper outlines four primary contributions:

Novel Adaptive Aggregation: An aggregation mechanism that utilizes differentially private client validation accuracies and HE to effectively address non-IID data distribution while ensuring privacy.
Hybrid Architecture: A unified classical-quantum model integrating CNNs for feature extraction with PQCs to enhance model expressivity in federated settings.
Efficient Dynamic Layer Sparing: A technique that reduces communication overhead by adaptively freezing less impactful classical layers while preserving the flexibility of quantum layers.
Theoretical Convergence Analysis: A formal proof establishing the convergence of the framework, accounting for the interplay of adaptive aggregation, layer sparing, and privacy mechanisms.

4. Experimental Results

Experiments were conducted on CIFAR-10, SVHN, and Fashion-MNIST datasets using 10 clients over 20 communication rounds with non-IID distributions (Dirichlet $\alpha=0.1$ ).

Performance: AdeptHEQ-FL (configured with 4 qubits and 2 layers) outperformed both a Standard-FedQNN and a state-of-the-art FHE-FedQNN across all datasets.
- On the complex CIFAR-10 dataset, AdeptHEQ-FL achieved an accuracy of 72.61%, representing an approximate 25.43% improvement over Standard-FedQNN (63.60%) and a 14.17% improvement over FHE-FedQNN (57.89%).
- Performance gains were observed on SVHN and Fashion-MNIST as well, though more modest.
Resource Efficiency: Despite using fewer resources (4 qubits, 2 layers) compared to the baselines (6 qubits, 6 layers), AdeptHEQ-FL achieved superior results. This is attributed to the adaptive aggregation strategy, which weights updates based on privatized accuracy rather than treating all clients equally, and the layer-freezing mechanism which reduces unnecessary communication.
Sensitivity: Reducing quantum resources further (e.g., 2 qubits, 1 layer) led to performance degradation, particularly on complex datasets, indicating that complex data requires sufficient quantum capacity.

5. Significance and Claims

The paper claims that AdeptHEQ-FL provides a comprehensive solution that unifies performance, privacy, and efficiency in a hybrid classical-quantum FL paradigm. Its significance lies in:

Synergistic Integration: Successfully combining quantum expressivity with formal privacy guarantees (DP and selective HE) and communication efficiency.
Non-IID Robustness: Demonstrating superior handling of non-IID data through accuracy-weighted aggregation, overcoming the limitations of uniform aggregation in existing QFL and FHE-based approaches.
Practicality: Offering a resource-aware design that reduces communication overhead via dynamic layer sparing while maintaining the adaptability of quantum components.

Limitations Acknowledged:
The authors note that HE is currently applied only to the final layer for tractability, leaving other layers unencrypted. The framework was evaluated in simulated environments and has not yet been tested on real-world quantum hardware. Additionally, the convergence analysis relies on assumptions of smoothness and bounded gradient variance that may not hold in highly non-convex settings. Future work is proposed to extend encryption coverage, test on physical devices, and generalize to larger datasets.