The concept of an autoencoder is a key element of modern machine learning methods. It is used, e.g., to compress the input data into a lower-dimensional representation, which is later employed in other machine learning algorithms. In the area of quantum computing application methods, quantum machine learning is also developing dynamically, with the concept of a quantum autoencoder also present. In the article, we discuss a variant of building a quantum autoencoder based on a quantum convolutional network. The proposed autoencoder is characterized by an architecture based on adjacent quantum gates, which is especially important for the near-future noisy intermediate-scale hardware implementation of such a type of quantum circuits. The proposed circuits are built with an elementary set of gates, i.e., controlled negation gates and rotation gates. The described architecture of a quantum autoencoder properly uses the quantum phenomenon called quantum exponential capacitys, i.e., a linear number of qubits which allow encoding an exponential amount of classical information. In our case, for n qubit, it is possible to encode a classical gray coloured image with dimensionality 2n × 2n. The conducted numerical experiments on a set image of handwritten characters and letters show that, for a small number of parameters, the quantum autoencoder offers a reconstruction quality comparable to the currently used classical autoencoders. An important assumption is the omission of additional dimensionality reduction techniques, e.g., PCA, for the preparation of classical data. In the discussed experiment, the data after reconstruction can be read directly from the quantum register, through a series of quantum register measurements.
The concept of an autoencoder is a key element of modern machine learning methods. It is used, e.g., to compress the input data into a lower-dimensional representation, which is later employed in other machine learning algorithms. In the area of quantum computing application methods, quantum machine learning is also developing dynamically, with the concept of a quantum autoencoder also present. In the article, we discuss a variant of building a quantum autoencoder based on a quantum convolutional network. The proposed autoencoder is characterized by an architecture based on adjacent quantum gates, which is especially important for the near-future noisy intermediate-scale hardware implementation of such a type of quantum circuits. The proposed circuits are built with an elementary set of gates, i.e., controlled negation gates and rotation gates. The described architecture of a quantum autoencoder properly uses the quantum phenomenon called quantum exponential capacitys, i.e., a linear number of qubits which allow encoding an exponential amount of classical information. In our case, for n qubit, it is possible to encode a classical gray coloured image with dimensionality 2n × 2n. The conducted numerical experiments on a set image of handwritten characters and letters show that, for a small number of parameters, the quantum autoencoder offers a reconstruction quality comparable to the currently used classical autoencoders. An important assumption is the omission of additional dimensionality reduction techniques, e.g., PCA, for the preparation of classical data. In the discussed experiment, the data after reconstruction can be read directly from the quantum register, through a series of quantum register measurements.
The autoencoder is one of machine learning algorithms used for feature extraction by dimension reduction of input data, denoising of images, and prior learning of neural networks. At the same time, autoencoders using quantum computers are also being developed. However, current quantum computers have a limited number of qubits, which makes it difficult to calculate big data. In this paper, as a solution to this problem, we propose a computation method that applies a convolution filter, which is one of the methods used in machine learning, to quantum computation. As a result of applying this method to a quantum autoencoder, we succeeded in denoising image data of several hundred qubits or more using only a few qubits under the autoencoding accuracy of 98%, and the effectiveness of this method was obtained. Meanwhile, we have verified the feature extraction function of the proposed autoencoder by dimensionality reduction. By projecting the MNIST data to two-dimension, we found the proposed method showed superior classification accuracy to the vanilla principle component analysis (PCA). We also verified the proposed method using IBM Q Melbourne and the actual machine failed to provide accurate results implying high error rate prevailing in the current NISQ quantum computer.
Abstract Quantum machine learning is one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era. We propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks (CNN), which greatly reduces the computing complexity compared with its classical counterparts, with O (( log 2 M ) 6 ) basic gates and O ( m 2 + e ) variational parameters, where M is the input data size, m is the filter mask size, and e is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the parameters are independent on the input sizes, making it friendly to near-term quantum devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied to image processing, and numerical simulation of three types of spatial filtering, image smoothing, sharpening, and edge detection is performed. Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of handwritten numbers. Compared with previous work, this machine learning model can provide implementable quantum circuits that accurately corresponds to a specific classical convolutional kernel. It provides an efficient avenue to transform CNN to QCNN directly and opens up the prospect of exploiting quantum power to process information in the era of big data.
Quantum convolutional neural networks (QCNNs) have become increasingly popular in quantum machine learning (QML) due to their efficient parameterization and hierarchical representation of quantum information. Anomaly detection is an important machine learning task with applications across a wide range of domains, including scientific data analysis. In this work, we adapt a QCNN architecture into a quantum autoencoder (QAE) framework for reconstruction-based anomaly detection. The models are trained in a semi-supervised manner on normal samples to reconstruct feature-extracted and dimensionally reduced time-series data, with reconstruction error used as an anomaly score. We investigate two quantum convolutional autoencoder architectures that differ in their treatment of latent information: a hierarchical architecture in which information remains distributed across the circuit and a bottleneck-based architecture in which information is explicitly compressed and reconstructed using additional decoder qubits. The size of the quantum latent space is varied to study its influence on reconstruction accuracy and anomaly detection performance. The approaches are benchmarked against both a variational quantum circuit and a comparable classical baseline using a real-world exoplanet anomaly-detection dataset. Results indicate a trade-off between latent-space size and model capacity, while also suggesting that explicit latent-space compression through a quantum bottleneck can improve anomaly detection performance relative to architectures that retain information throughout the circuit.
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.
In recent years, machine learning and deep learning have driven advances in domains such as image classification, speech recognition, and anomaly detection by leveraging multi-layer neural networks to model complex data. Simultaneously, quantum computing (QC) promises to address classically intractable problems via quantum parallelism, motivating research in quantum machine learning (QML). Among QML techniques, quantum autoencoders show promise for compressing high-dimensional quantum and classical data. However, designing effective quantum circuit architectures for quantum autoencoders remains challenging due to the complexity of selecting gates, arranging circuit layers, and tuning parameters.
This paper proposes a neural architecture search (NAS) framework that automates the design of quantum autoencoders using a genetic algorithm (GA). By systematically evolving variational quantum circuit (VQC) configurations, our method seeks to identify high-performing hybrid quantum-classical autoencoders for data reconstruction without becoming trapped in local minima. We demonstrate effectiveness on image datasets, highlighting the potential of quantum autoencoders for efficient feature extraction within a noise-prone, near-term quantum era. Our approach lays a foundation for broader application of genetic algorithms to quantum architecture search, aiming for a robust, automated method that can adapt to varied data and hardware constraints.
Quantum Autoencoders emerge as a revolutionary framework in the field of data compression and feature learning, harnessing the unique advantages of quantum computing to enhance classical methodologies. This chapter explores the architecture and operational principles of quantum autoencoders, detailing their ability to efficiently compress high-dimensional data while retaining essential features. By leveraging quantum superposition and entanglement, these autoencoders surpass traditional techniques, offering improved performance in data representation and reconstruction tasks. Applications across various domains, including image processing, natural language processing, and genomics, are examined to highlight the versatility and effectiveness of quantum autoencoders. Additionally, the chapter addresses the challenges posed by current quantum hardware limitations and outlines future research directions aimed at optimizing the performance of these innovative models. The findings indicate that quantum autoencoders hold significant potential to transform data processing landscapes, making them a pivotal area for future exploration in quantum machine learning.