Quantum convolutional neural network (QCNN), an early application for quantum computers in the noisy intermediate-scale quantum era, has been consistently proven successful as a machine learning (ML) algorithm for several tasks with significant accuracy. Derived from its classical counterpart, QCNN is prone to overfitting. Overfitting is a typical shortcoming of ML models that are trained too closely to the availed training dataset and perform relatively poorly on unseen datasets for a similar problem. In this work we study post-training approaches for mitigating overfitting in QCNNs. We find that a straightforward adaptation of a classical post-training method, known as neuron dropout, to the quantum setting leads to a significant and undesirable consequence: a substantial decrease in success probability of the QCNN. We argue that this effect exposes the crucial role of entanglement in QCNNs and the vulnerability of QCNNs to entanglement loss. Hence, we propose a parameter adaptation method as an alternative method. Our method is computationally efficient and is found to successfully handle overfitting in the test cases.
Quantum convolutional neural network (QCNN), an early application for quantum computers in the noisy intermediate-scale quantum era, has been consistently proven successful as a machine learning (ML) algorithm for several tasks with significant accuracy. Derived from its classical counterpart, QCNN is prone to overfitting. Overfitting is a typical shortcoming of ML models that are trained too closely to the availed training dataset and perform relatively poorly on unseen datasets for a similar problem. In this work we study post-training approaches for mitigating overfitting in QCNNs. We find that a straightforward adaptation of a classical post-training method, known as neuron dropout, to the quantum setting leads to a significant and undesirable consequence: a substantial decrease in success probability of the QCNN. We argue that this effect exposes the crucial role of entanglement in QCNNs and the vulnerability of QCNNs to entanglement loss. Hence, we propose a parameter adaptation method as an alternative method. Our method is computationally efficient and is found to successfully handle overfitting in the test cases.
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.
Abstract In classical machine learning (ML), “overfitting” is the phenomenon occurring when a given model learns the training data excessively well, and it thus performs poorly on unseen data. A commonly employed technique in ML is the so called “dropout,” which prevents computational units from becoming too specialized, hence reducing the risk of overfitting. With the advent of quantum neural networks (QNNs) as learning models, overfitting might soon become an issue, owing to the increasing depth of quantum circuits as well as multiple embedding of classical features, which are employed to give the computational nonlinearity. Here, a generalized approach is presented to apply the dropout technique in QNN models, defining and analyzing different quantum dropout strategies to avoid overfitting and achieve a high level of generalization. This study allows to envision the power of quantum dropout in enabling generalization, providing useful guidelines on determining the maximal dropout probability for a given model, based on overparametrization theory. It also highlights how quantum dropout does not impact the features of the QNN models, such as expressibility and entanglement. All these conclusions are supported by extensive numerical simulations and may pave the way to efficiently employing deep quantum machine learning (QML) models based on state‐of‐the‐art QNNs.
From self-driving cars to medical diagnoses, machine learning (ML) has revolutionized our world in the last few decades. Additionally, Quantum Computing has considerable promise for the future, with superposition and entanglement making quantum algorithms much more efficient and effective than their classical counterparts. Quantum ML aims to apply these quantum principles to the groundbreaking field of ML, such as for image classification. Convolutional Neural Networks (CNNs) are very effective for classification, so we study a Quantum Convolutional Neural Network (QCNN) that is trained to distinguish between handwritten numbers in the MNIST dataset and compared to a similar-sized classical network. After tuning the QCNN and quantum encoding, the QCNN achieved comparable accuracy to the classical network.
Quantum Machine Learning (QML) has been acknowledged for its transformative potential in enhancing computational capabilities beyond classical approaches, with Quantum Neural Networks (QNNs) emerging as one of the most promising models. Despite the advancements, the adaptation of effective optimization techniques such as batch normalization or regularization, which are well-established in classical Neural Networks, remains an ongoing challenge for QNNs.This adaptation is crucial, especially when considering the implementation of techniques like quantum dropout, which, although inspired by its classical counterpart to reduce the risk of overfitting by "deleting" certain model components during the forward step, exhibits distinct behaviours in a quantum context. This study introduces a novel approach to modulate the impact of dropout in QNNs through a technique we term Soft Dropout. Our method introduces a parameterized softening mechanism for gate eliminations, enabling a more nuanced control over the dropout process, thereby mitigating its adverse effects on the network’s learning capacity, and reducing at the same time the risk of overfitting.Our experimental analysis demonstrates that softening current quantum dropout consistently enhances model performance across a spectrum of configurations. This improvement is attributed to the intrinsic properties of quantum gates, which allow for a gradual adjustment of their impact on the quantum circuit up to the identity operation. The results highlight the importance of adapting classical machine learning techniques to the quantum context, considering the unique computational model of quantum processing, potentially accelerating the adoption of QML in real-world problems.
Abstract Quantum machine learning has achieved great success in many areas of image classification, however, in the Noisy Intermediate-Scale Quantum (NISQ) era, most of the quantum machine learning experimental results are obtained from simulations on classical computers, and most of the experimental environments do not take into account the detrimental effects of quantum noise on quantum classifiers. In fact, the prevalent quantum noise, such as Depolarization, Phase flip, etc., has the potential to significantly undermine the classification performance of quantum circuits. Addressing the challenge of mitigating the disturbing impact of quantum noise on quantum neural networks has become a prominent research focus in recent years. In this paper, we propose a Noise Mitigation method based on the image classification task, which is deployed on the constructed quantum convolutional neural network with noise, aiming to improve the classification accuracy by using Noise Mitigation to reduce the expressibility of quantum circuits. The designed Noise Mitigation method can adjust the parameters according to the complexity of the circuit to achieve better results. Numerical simulations conducted on the MNIST and Fashion-MNIST datasets substantiate the efficacy of the proposed methodology.
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.