Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.16117 · IET conference proceedings.

A differentially private quantum neural network for probabilistic optimal power flow

Yuji Cao, Yue Chen, Yan Hui Xu

Published Mar 1, 2025• 1 citation
arXivHTMLPDF

Abstract

The stochastic nature of renewable energy and load demand requires efficient and accurate solutions for probabilistic optimal power flow (OPF). Quantum neural networks (QNNs), which combine quantum computing and machine learning, offer computational advantages in approximating OPF by effectively handling high-dimensional data. However, adversaries with access to non-private OPF solutions can potentially infer sensitive load demand patterns, raising significant privacy concerns. To address this issue, we propose a privacy-preserving QNN model for probabilistic OPF approximation. By incorporating Gaussian noise into the training process, the learning algorithm achieves (ɛ, δ)-differential privacy with theoretical guarantees. Moreover, we develop a strongly entangled quantum state to enhance the nonlinearity expressiveness of the QNN. Experimental results demonstrate that the proposed method successfully prevents privacy leakage without compromising the statistical properties of probabilistic OPF. Moreover, compared to classical private neural networks, the QNN reduces the number of parameters by 90% while achieving significantly higher accuracy and greater stability.

DOI
10.1049/icp.2025.0552

Related papers

Quantum machine learning with differential privacy

William M. Watkins, Samuel Yen-Chi Chen, Shinjae Yoo

Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach's success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

arXiv:2103.06232•Scientific Reports•Feb 11, 2023•83 citations

Quantum neural network classifier with differential privacy

Guodong Li, Fangce Yu, Qingle Wang +3 more

Abstract Quantum neural networks (QNN) hold the potential for quantum advantages but are confronted with privacy leakage risks that could undermine users’ benefits. To address this issue, we propose an enhanced QNN model integrated with differential privacy. After converting classical data into quantum states using encoding circuit, we apply data re-uploading technology to embed the encoding circuit multiple times into the overall circuit. The classification outcomes are derived by measuring the final quantum state. During the optimization process of QNN, we introduce Gaussian noise into the gradient of the loss function to ensure differential privacy. Our theoretical analysis demonstrates that in differential privacy settings, the model effectively protects privacy while demonstrating good performance. Our experimental analysis demonstrates that on four standard datasets, our model achieves the same accuracy as classical neural network (NN) while utilizing only 22% of the parameters of NN, and exhibiting lower performance loss compared to other QNN.

Physica Scripta•Feb 4, 2025•2 citations

Quantum-Enabled Probabilistic Optimal Power Flow with Built-in Differential Privacy

Yuji Cao, Tongxin Li, Yue Chen

Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose a qubit-efficient framework for solving a crucial power system optimization problem, the probabilistic optimal power flow (POPF). We demonstrate that quantum noise, traditionally viewed as a drawback, can in fact be leveraged to provide a built-in differential privacy (DP) guarantee. Specifically, we first linearize POPF into a multi-parametric linear program (MP-LP) with renewable uncertainties being the parameters. This decomposes the parameter space into critical regions with precomputed solution maps. Second, a variational quantum circuit (VQC) classifies the critical region based on each uncertainty realization and then recovers the final solution. In this way, the required qubits scale with the uncertain parameters instead of the network size, with only 5 qubits versus 600+ for direct quantum OPF in a 69-bus system. Moreover, we prove the depolarizing noise of VQC provides DP guarantees and characterize the privacy-cost tradeoff. Case studies validate the proposed VQC achieves 2.1$\times$ smaller privacy budgets compared to its classical counterpart. At matched privacy levels, the VQC also maintains lower infeasibility and prediction error.

arXiv:2603.16780•Mar 17, 2026•0 citations

Hybrid quantum convolutional neural network with differential privacy for image classification

Bai Liu, Hao Chen, Shuheng Qi

Quantum convolutional neural networks hold potential advantages for image recognition by exploiting unique quantum properties. However, their training processes remain susceptible to privacy leakage. To address this issue, we propose a hybrid quantum convolutional neural network (HQCNN) model with differential privacy. This architecture utilizes quantum superposition and entanglement to efficiently extract image features. To ensure differential privacy, Gaussian noise is added to the parameter gradients. Crucially, the superior feature extraction and learning capabilities of the HQCNN are utilized to mitigate the performance degradation typically induced by noise injection. Experiments on the MNIST and Fashion-MNIST datasets demonstrate that the proposed model achieves a test accuracy exceeding 95% under a strict privacy budget of ɛ < 1.04. Furthermore, evaluations on the CIFAR-10 dataset confirm the feasibility of the model in the differentially private scenario. Comparative analyses further validate that the proposed model preserves privacy while maintaining superior performance in differentially private training.

AIP Advances•Mar 1, 2026•0 citations

A Framework for Hybrid-Quantum Neural Networks for Anomaly Detection and Optimization in Smart Grids: Challenges and Opportunities

Irene Kahvazadeh, A.C. Fong, Guan Hong

With increasing prevalence of distributed energy resources (DERs), the growing threat of cyber-physical attacks, and the need for real-time optimization present major challenges for modern smart grids. With challenges also come opportunities. Although classical machine learning (ML) models, such as deep neural networks (DNNs), have shown promise toward meeting some of these challenges, they often struggle with the computational complexity when vast volumes of grid data are involved. The problems are particularly acute in situations when real-time responses are essential. This paper proposes a framework that integrates classical and quantum neural networks (QNNs) to initiate a new paradigm of time-sensitive grid management. We explore the potential of quantum computing to enhance the capabilities of classical neural networks in two critical applications: (1) real-time anomaly detection for cybersecurity and (2) dynamic optimal power flow (OPF) management for grid stability. We propose a hybrid quantum-classical neural network framework suitable for near-term quantum devices, discuss the theoretical advantages in computational speed and model capacity, and address the significant challenges related to quantum hardware noise, algorithmic design, and data encoding. The framework is flexible enough to allow for futureproofing as QNNs and quantum computing hardware continue to evolve. Our analysis suggests that QNNs, even in their current nascent stage, hold great promise to revolutionize smart grid analytics by solving complex, time-sensitive classification and optimization problems that are currently difficult or intractable for classical methods. The study therefore lays the groundwork for a future smart grid that is more secure, efficient, and robust.

Asia-Pacific Power and Energy Engineering Conference (APPEEC)•Dec 2, 2025•0 citations

Q-ShiftDP: A Differentially Private Parameter-Shift Rule for Quantum Machine Learning

Hoang M. Ngo, Nhat Hoang-Xuan, Quan Nguyen +3 more

Quantum Machine Learning (QML) promises significant computational advantages, but preserving training data privacy remains challenging. Classical approaches like differentially private stochastic gradient descent (DP-SGD) add noise to gradients but fail to exploit the unique properties of quantum gradient estimation. In this work, we introduce the Differentially Private Parameter-Shift Rule (Q-ShiftDP), the first privacy mechanism tailored to QML. By leveraging the inherent boundedness and stochasticity of quantum gradients computed via the parameter-shift rule, Q-ShiftDP enables tighter sensitivity analysis and reduces noise requirements. We combine carefully calibrated Gaussian noise with intrinsic quantum noise to provide formal privacy and utility guarantees, and show that harnessing quantum noise further improves the privacy-utility trade-off. Experiments on benchmark datasets demonstrate that Q-ShiftDP consistently outperforms classical DP methods in QML.

arXiv:2602.02962•Feb 3, 2026•0 citations
The stochastic nature of renewable energy and load demand requires efficient and accurate solutions for probabilistic optimal power flow (OPF). Quantum neural networks (QNNs), which combine quantum computing and machine learning, offer computational advantages in approximating OPF by effectively handling high-dimensional data. However, adversaries with access to non-private OPF solutions can potentially infer sensitive load demand patterns, raising significant privacy concerns. To address this issue, we propose a privacy-preserving QNN model for probabilistic OPF approximation. By incorporating Gaussian noise into the training process, the learning algorithm achieves (ɛ, δ)-differential privacy with theoretical guarantees. Moreover, we develop a strongly entangled quantum state to enhance the nonlinearity expressiveness of the QNN. Experimental results demonstrate that the proposed method successfully prevents privacy leakage without compromising the statistical properties of probabilistic OPF. Moreover, compared to classical private neural networks, the QNN reduces the number of parameters by 90% while achieving significantly higher accuracy and greater stability.
Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach's success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.
Abstract Quantum neural networks (QNN) hold the potential for quantum advantages but are confronted with privacy leakage risks that could undermine users’ benefits. To address this issue, we propose an enhanced QNN model integrated with differential privacy. After converting classical data into quantum states using encoding circuit, we apply data re-uploading technology to embed the encoding circuit multiple times into the overall circuit. The classification outcomes are derived by measuring the final quantum state. During the optimization process of QNN, we introduce Gaussian noise into the gradient of the loss function to ensure differential privacy. Our theoretical analysis demonstrates that in differential privacy settings, the model effectively protects privacy while demonstrating good performance. Our experimental analysis demonstrates that on four standard datasets, our model achieves the same accuracy as classical neural network (NN) while utilizing only 22% of the parameters of NN, and exhibiting lower performance loss compared to other QNN.
Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose a qubit-efficient framework for solving a crucial power system optimization problem, the probabilistic optimal power flow (POPF). We demonstrate that quantum noise, traditionally viewed as a drawback, can in fact be leveraged to provide a built-in differential privacy (DP) guarantee. Specifically, we first linearize POPF into a multi-parametric linear program (MP-LP) with renewable uncertainties being the parameters. This decomposes the parameter space into critical regions with precomputed solution maps. Second, a variational quantum circuit (VQC) classifies the critical region based on each uncertainty realization and then recovers the final solution. In this way, the required qubits scale with the uncertain parameters instead of the network size, with only 5 qubits versus 600+ for direct quantum OPF in a 69-bus system. Moreover, we prove the depolarizing noise of VQC provides DP guarantees and characterize the privacy-cost tradeoff. Case studies validate the proposed VQC achieves 2.1×\times× smaller privacy budgets compared to its classical counterpart. At matched privacy levels, the VQC also maintains lower infeasibility and prediction error.
Quantum convolutional neural networks hold potential advantages for image recognition by exploiting unique quantum properties. However, their training processes remain susceptible to privacy leakage. To address this issue, we propose a hybrid quantum convolutional neural network (HQCNN) model with differential privacy. This architecture utilizes quantum superposition and entanglement to efficiently extract image features. To ensure differential privacy, Gaussian noise is added to the parameter gradients. Crucially, the superior feature extraction and learning capabilities of the HQCNN are utilized to mitigate the performance degradation typically induced by noise injection. Experiments on the MNIST and Fashion-MNIST datasets demonstrate that the proposed model achieves a test accuracy exceeding 95% under a strict privacy budget of ɛ < 1.04. Furthermore, evaluations on the CIFAR-10 dataset confirm the feasibility of the model in the differentially private scenario. Comparative analyses further validate that the proposed model preserves privacy while maintaining superior performance in differentially private training.
With increasing prevalence of distributed energy resources (DERs), the growing threat of cyber-physical attacks, and the need for real-time optimization present major challenges for modern smart grids. With challenges also come opportunities. Although classical machine learning (ML) models, such as deep neural networks (DNNs), have shown promise toward meeting some of these challenges, they often struggle with the computational complexity when vast volumes of grid data are involved. The problems are particularly acute in situations when real-time responses are essential. This paper proposes a framework that integrates classical and quantum neural networks (QNNs) to initiate a new paradigm of time-sensitive grid management. We explore the potential of quantum computing to enhance the capabilities of classical neural networks in two critical applications: (1) real-time anomaly detection for cybersecurity and (2) dynamic optimal power flow (OPF) management for grid stability. We propose a hybrid quantum-classical neural network framework suitable for near-term quantum devices, discuss the theoretical advantages in computational speed and model capacity, and address the significant challenges related to quantum hardware noise, algorithmic design, and data encoding. The framework is flexible enough to allow for futureproofing as QNNs and quantum computing hardware continue to evolve. Our analysis suggests that QNNs, even in their current nascent stage, hold great promise to revolutionize smart grid analytics by solving complex, time-sensitive classification and optimization problems that are currently difficult or intractable for classical methods. The study therefore lays the groundwork for a future smart grid that is more secure, efficient, and robust.
Quantum Machine Learning (QML) promises significant computational advantages, but preserving training data privacy remains challenging. Classical approaches like differentially private stochastic gradient descent (DP-SGD) add noise to gradients but fail to exploit the unique properties of quantum gradient estimation. In this work, we introduce the Differentially Private Parameter-Shift Rule (Q-ShiftDP), the first privacy mechanism tailored to QML. By leveraging the inherent boundedness and stochasticity of quantum gradients computed via the parameter-shift rule, Q-ShiftDP enables tighter sensitivity analysis and reduces noise requirements. We combine carefully calibrated Gaussian noise with intrinsic quantum noise to provide formal privacy and utility guarantees, and show that harnessing quantum noise further improves the privacy-utility trade-off. Experiments on benchmark datasets demonstrate that Q-ShiftDP consistently outperforms classical DP methods in QML.