Quantum autoencoder, as a quantum machine learning algorithm, provides an important research direction for image compression. This paper proposes a quantum autoencoder specifically designed for image compression. We first use feature mapping to store images as quantum states and propose a new parameterized quantum circuit and a pre-training method. After pre-training, a reference state is determined and the circuit parameters are updated through further training. Finally, we experimentally validate the quantum autoencoder. For reconstructed 10-qubit images, the fidelity reaches 0.98 and the SSIM reaches 0.927. For reconstructed 10-qubit noisy images, the PSNR improves by 1.4[Formula: see text]dB. Simulation results demonstrate that the proposed quantum autoencoder efficiently compresses quantum images while also possessing denoising capabilities.
Quantum autoencoder, as a quantum machine learning algorithm, provides an important research direction for image compression. This paper proposes a quantum autoencoder specifically designed for image compression. We first use feature mapping to store images as quantum states and propose a new parameterized quantum circuit and a pre-training method. After pre-training, a reference state is determined and the circuit parameters are updated through further training. Finally, we experimentally validate the quantum autoencoder. For reconstructed 10-qubit images, the fidelity reaches 0.98 and the SSIM reaches 0.927. For reconstructed 10-qubit noisy images, the PSNR improves by 1.4[Formula: see text]dB. Simulation results demonstrate that the proposed quantum autoencoder efficiently compresses quantum images while also possessing denoising capabilities.
Abstract Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It ensures the preservation of image quality and accurate interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This paper proposes a method, the quantum convolutional autoencoder (QCAE), which enhances traditional convolutional autoencoders by replacing their latent space with a quantum counterpart implemented via a quantum approximate optimization algorithm (QAOA)-inspired ansatz circuit. To enhance efficiency, we leveraged the advantages of the QAOA-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.
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.
As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to achieve automatic data compression in the field of quantum information. Such a quantum autoencoder can be implemented through training the parameters of a quantum device using classical optimization algorithms. In this paper, we demonstrate the condition of achieving a perfect quantum autoencoder and theoretically prove that a quantum autoencoder can losslessly compress high-dimensional quantum information into a low-dimensional space (also called latent space) if the number of maximum linearly independent vectors from input states is no more than the dimension of the latent space. Also, we experimentally realize a universal two-qubit unitary gate and design a quantum autoencoder device by applying a machine learning method. Experimental results demonstrate that our quantum autoencoder is able to compress two two-qubit states into two one-qubit states. Besides compressing quantum information, the quantum autoencoder is used to experimentally discriminate two groups of nonorthogonal states.
Abstract Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x , to map x to a lower dimensional point y such that x can likely be recovered from y . The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.
Quantum machine learning methods often rely on fixed, hand-crafted quantum encodings that may not capture optimal features for downstream tasks. In this work, we study the power of quantum autoencoders in learning data-driven quantum representations. We first theoretically demonstrate that the quantum autoencoder method is efficient in terms of sample complexity throughout the entire training process. Then we numerically train the quantum autoencoder on 3 million peptide sequences, and evaluate their effectiveness across multiple peptide classification problems including antihypertensive peptide prediction, blood-brain barrier-penetration, and cytotoxic activity detection. The learned representations were compared against Hamiltonian-evolved baselines using a quantum kernel with support vector machines. Results show that quantum autoencoder learned representations achieve accuracy improvements ranging from 0.4\% to 8.1\% over Hamiltonian baselines across seven datasets, demonstrating effective generalization to diverse downstream datasets with pre-training enabling effective transfer learning without task-specific fine-tuning. This work establishes that quantum autoencoder architectures can effectively learn from large-scale datasets (3 million samples) with compact parameterizations ($\sim$900 parameters), demonstrating their viability for practical quantum applications.
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.