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arXiv:2410.19921 · Advanced Quantum Technologies

Method for Noise‐Induced Regularization in Quantum Neural Networks

Viacheslav Kuzmin, W. Somogyi, Ekaterina Aleksandrovna Pankovets, Alexey A. Melnikov

Published Nov 28, 2025• 3 citations
arXivHTMLPDF

Abstract

ABSTRACT In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are subject to, and in algorithm design, a large effort is underway to provide scalable error correction or mitigation techniques. Yet some previous work has indicated that certain classes of quantum algorithms, such as quantum machine learning, may, in fact, be intrinsically robust to or even benefit from the presence of a small amount of noise. Here, we demonstrate that noise levels in quantum hardware can be effectively tuned to enhance the ability of quantum neural networks to generalize data, acting akin to regularisation in classical neural networks. As an example, we consider two regression tasks, where, by tuning the noise level in the circuit, we demonstrated improvement of the validation mean squared error loss. Moreover, we demonstrate the method's effectiveness by numerically simulating QNN training on a realistic model of a noisy superconducting quantum computer.

DOI
10.1002/qute.202400603

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ABSTRACT In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are subject to, and in algorithm design, a large effort is underway to provide scalable error correction or mitigation techniques. Yet some previous work has indicated that certain classes of quantum algorithms, such as quantum machine learning, may, in fact, be intrinsically robust to or even benefit from the presence of a small amount of noise. Here, we demonstrate that noise levels in quantum hardware can be effectively tuned to enhance the ability of quantum neural networks to generalize data, acting akin to regularisation in classical neural networks. As an example, we consider two regression tasks, where, by tuning the noise level in the circuit, we demonstrated improvement of the validation mean squared error loss. Moreover, we demonstrate the method's effectiveness by numerically simulating QNN training on a realistic model of a noisy superconducting quantum computer.
Quantum Neural Network (QNN) is a promising application towards quantum advantage on near-term quantum hardware. However, due to the large quantum noises (errors), the performance of QNN models has a severe degradation on real quantum devices. For example, the accuracy gap between noise-free simulation and noisy results on IBMQ-Yorktown for MNIST-4 classification is over 60%. Existing noise mitigation methods are general ones without leveraging unique characteristics of QNN and are only applicable to inference; on the other hand, existing QNN work does not consider noise effect. To this end, we present RoQNN, a QNN-specific framework to perform noise-aware optimizations in both training and inference stages to improve robustness. We analytically deduct and experimentally observe that the effect of quantum noise to QNN measurement outcome is a linear map from noise-free outcome with a scaling and a shift factor. Motivated by that, we propose post-measurement normalization to mitigate the feature distribution differences between noise-free and noisy scenarios. Furthermore, to improve the robustness against noise, we propose noise injection to the training process by inserting quantum error gates to QNN according to realistic noise models of quantum hardware. Finally, post-measurement quantization is introduced to quantize the measurement outcomes to discrete values, achieving the denoising effect. Extensive experiments on 8 classification tasks using 6 quantum devices demonstrate that RoQNN improves accuracy by up to 43%, and achieves over 94% 2-class, 80% 4-class, and 34% 10-class MNIST classification accuracy measured on real quantum computers. We also open-source our PyTorch library for construction and noise-aware training of QNN at this https URL .
Abstract The rapid advancements in machine learning and quantum computing have given rise to a new research frontier: quantum machine learning. Quantum models designed for tackling classification problems possess the potential to deliver speed enhancements and superior predictive accuracy compared to their classical counterparts. However, recent research has revealed that quantum neural networks (QNNs), akin to their classical deep neural network-based classifier counterparts, are vulnerable to adversarial attacks. In these attacks, meticulously designed perturbations added to clean input data can result in QNNs producing incorrect predictions with high confidence. To mitigate this issue, we suggest enhancing the adversarial robustness of quantum machine learning systems by incorporating noise layers into QNNs. This is accomplished by solving a Min-Max optimization problem to control the magnitude of the noise, thereby increasing the QNN’s resilience against adversarial attacks. Extensive numerical experiments illustrate that our proposed method outperforms state-of-the-art defense techniques in terms of both clean and robust accuracy.
Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations, thus introducing fundamental finite-sampling noise even on error-free quantum computers. We reduce this noise by introducing the variance regularization, a technique for reducing the variance of the expectation value during the quantum model training. This technique requires no additional circuit evaluations if the QNN is properly constructed. Our empirical findings demonstrate the reduced variance speeds up the training and lowers the output noise as well as decreases the number of necessary evaluations of gradient circuits. This regularization method is benchmarked on the regression of multiple functions and the potential energy surface of water. We show that in our examples, it lowers the variance by an order of magnitude on average and leads to a significantly reduced noise level of the QNN. We finally demonstrate QNN training on a real quantum device and evaluate the impact of error mitigation. Here, the optimization is feasible only due to the reduced number of necessary shots in the gradient evaluation resulting from the reduced variance.
A quantum error mitigation technique based on machine learning is proposed, which learns how to adjust the probabilities estimated by measurement in the computational basis. Neural networks in two different designs are trained with random quantum circuits consisting of a set of one- and two-qubit unitary gates whose measurement statistics in the ideal (noiseless) and real (noisy) cases are known. Once the neural networks are trained, they infer the amount of probability adjustment to be made on the measurement obtained from executing an unseen quantum circuit to reduce the error. The proposed schemes are tested with two-, three-, five-, and seven-qubit quantum circuits of depth up to 20 by computer simulations with realistic error models and experiments using the IBM quantum cloud platform. In all test cases, the proposed mitigation technique reduces the error effectively. Our method can be used to improve the accuracy of noisy intermediate-scale quantum (NISQ) algorithms without relying on extensive error characterization or quantum error correction.
Abstract Quantum computing holds transformative promise, but its realization is hindered by the inherent susceptibility of quantum computers to errors. Quantum error mitigation has proved to be an enabling way to reduce computational error in present noisy intermediate scale quantum computers. This research introduces an innovative approach to quantum error mitigation by leveraging machine learning, specifically employing adaptive neural networks. With experiment and simulations done on 127-qubit IBM superconducting quantum computer, we were able to develop and train a neural network architecture to dynamically adjust output expectation values based on error characteristics. The model leverages a prior classifier module outcome on simulated quantum circuits with errors, and the antecedent neural network regression module adapts its parameters and response to each error characteristics. Results demonstrate the adaptive neural network’s efficacy in mitigating errors across diverse quantum circuits and noise models, showcasing its potential to surpass traditional error mitigation techniques with an accuracy of 99% using the fully adaptive neural network for quantum error mitigation. This work presents a significant application of classical machine learning methods towards enhancing the robustness and reliability of quantum computations, providing a pathway for the practical realization of quantum computing technologies.
Quantum computing has gained significant attention in recent years, with numerous algorithms and applications under active development. Limited by the current quantum technology, quantum noise and readout error have become critical issues. Various methods have been proposed to address readout error through error mitigation techniques, typically involving post-processing of measurement data. However, most of these methods increase the quantum hardware overhead, leading to higher computational costs. In this work, we present a machine-learning-based approach that minimizes hardware overhead while improving accuracy of the measurement probability distributions. We employed a convolutional neural network (CNN) autoencoder, commonly used for image denoising, as our baseline model. The datasets were derived from 4-qubit random circuits with depths ranging from 1 to 18, generated using Qiskit backends for target and noisy measurement data. The model was trained using mean squared error (MSE) as the loss function and Adam optimizer over 500 epochs, achieving an average noise reduction by 95% across the validation set, with no signs of overfitting. To validate the model's effectiveness across diverse quantum states, we conducted extensive tests on both typical quantum circuits and algorithms, including Grover's search algorithm, Quantum Fourier Transform, Haar random circuits and Trivial Paramagnet. The results demonstrated consistent and robust denoising in noisy measurement data, indicating that the autoencoder model is well-suited for efficient quantum error mitigation for current noisy quantum computers. This work contributes to the advancement of quantum error mitigation techniques using machine learning.