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arXiv:2602.12712

Reverse Delegated Training and Private Inference via Perfectly-Secure Quantum Homomorphic Encryption

Sergio A. Ortega, Miguel A. Martin-Delgado

quant-phcs.NESubmitted Feb 13, 2026• Announced Feb 16, 2026• 0 citations
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Abstract

Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+$T$ decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.

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RevTex 4.2, 19 pages, 11 color figures

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Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+TTT decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.
Abstract Quantum machine learning is expected to utilize the potential advantages of quantum computing to advance the efficiency of machine learning. However, with the help of quantum cloud servers, ordinary users may confront the threat of privacy leakage of input data and models when performing the training or inference of quantum neural networks (QNNs). To address this problem, we present a new framework that allows the training and inference of delegated QNNs to be performed on encrypted data to protect the privacy of users’ data and models. This framework contains two models that are alternately trained: an encryptor and a predictor. The classical client first trains the encryptor defined by a classical neural network to map plaintext input data to vastly different ciphertext data. The ciphertext data is sent to the quantum cloud server to train the predictor defined by a QNN, which can indirectly predict the labels of plaintext data. With the trained encryptor and predictor, the client can send the encrypted data to the server for prediction and obtain almost equivalent prediction results. The proposed framework is applied to three types of QNN models, each dealing with low-dimensional tabular data, image data, and one-dimensional time series data, respectively. Experimental results show that the privacy protection method based on our framework can protect data and model privacy without degrading the performance of QNNs. The framework does not require users to have quantum capabilities and is suitable for protecting data and model privacy for various QNN models.
Abstract Quantum learning models hold the potential to bring computational advantages over the classical realm. As powerful quantum servers become available on the cloud, ensuring the protection of clients’ private data becomes crucial. By incorporating quantum homomorphic encryption schemes, we present a general framework that enables quantum delegated and federated learning with a computation-theoretical data privacy guarantee. We show that learning and inference under this framework feature substantially lower communication complexity compared with schemes based on blind quantum computing. In addition, in the proposed quantum federated learning scenario, there is less computational burden on local quantum devices from the client side, since the server can operate on encrypted quantum data without extracting any information. We further prove that certain quantum speedups in supervised learning carry over to private delegated learning scenarios employing quantum kernel methods. Our results provide a valuable guide toward privacy-guaranteed quantum learning on the cloud, which may benefit future studies and security-related applications.
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Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.
Abstract It takes a lot of computational resources to train a machine learning model. So does quantum machine learning. In the NISQ (Noisy Intermediate Scale Quantum) era, there is a need for users who cannot afford quantum computers to utilize quantum servers to complete quantum machine learning with protection privacy of data and model parameters. In this paper, novel homomorphic encryption methods and circuit design with hidden parameter for R z , R x and R y gate are putting forward. Based on which, we further propose quantum neural network (QNN) with privacy protection of input data and training parameters, where hiding model parameters has hardly mentioned in existing literature. To verify the validity of the proposed scheme, we conducted experiments on MNIST and Iris datasets, and obtained losses and accuracy that are almost identical to the original algorithms. Experiments show that our scheme can protect privacy well in the training and have no effect on accuracy of the algorithm. By comparison, the proposed scheme is more secure than most existing literature and requires less extra complexity O(4n).
Quantum Federated Learning (QFL) enables distributed training of Quantum Machine Learning (QML) models by sharing model gradients instead of raw data. However, these gradients can still expose sensitive user information. To enhance privacy, homomorphic encryption of parameters has been proposed as a solution in QFL and related frameworks. In this work, we evaluate the overhead introduced by Fully Homomorphic Encryption (FHE) in QFL setups and assess its feasibility for real-world applications. We implemented various QML models including a Quantum Convolutional Neural Network (QCNN) trained in a federated environment with parameters encrypted using the CKKS scheme. This work marks the first QCNN trained in a federated setting with CKKS-encrypted parameters. Models of varying architectures were trained to predict brain tumors from MRI scans. The experiments reveal that memory and communication overhead remain substantial, making FHE challenging to deploy. Minimizing overhead requires reducing the number of model parameters, which, however, leads to a decline in classification performance, introducing a trade-off between privacy and model complexity.