Reducing noise in quantum systems is a significant challenge in advancing quantum technologies. We propose and demonstrate a noise reduction scheme utilizing a quantum autoencoder, which offers rigorous performance guarantees. The quantum autoencoder is trained to compress noisy quantum states into a latent subspace and eliminate noise through projective measurements. We identify various noise models in which the noiseless state can be perfectly reconstructed, even at high noise levels. We apply the autoencoder to cool thermal states to the ground state and reduce the cost of magic state distillation by several orders of magnitude. Our autoencoder can be implemented using only unitary transformations without the need for ancillas, making it immediately compatible with state-of-the-art quantum technologies. We experimentally validate our noise reduction methods in a photonic integrated circuit. Our results have direct applications in enhancing the robustness of quantum technologies against noise.
Reducing noise in quantum systems is a significant challenge in advancing quantum technologies. We propose and demonstrate a noise reduction scheme utilizing a quantum autoencoder, which offers rigorous performance guarantees. The quantum autoencoder is trained to compress noisy quantum states into a latent subspace and eliminate noise through projective measurements. We identify various noise models in which the noiseless state can be perfectly reconstructed, even at high noise levels. We apply the autoencoder to cool thermal states to the ground state and reduce the cost of magic state distillation by several orders of magnitude. Our autoencoder can be implemented using only unitary transformations without the need for ancillas, making it immediately compatible with state-of-the-art quantum technologies. We experimentally validate our noise reduction methods in a photonic integrated circuit. Our results have direct applications in enhancing the robustness of quantum technologies against noise.
Quantum autoencoder is an efficient variational quantum algorithm for quantum data compression. However, previous quantum autoencoders fail to compress and recover high-rank mixed states. In this work, we discuss the fundamental properties and limitations of the standard quantum-autoencoder model in more depth, and provide an information-theoretic solution to its recovering fidelity. Based on this understanding, we present a noise-assisted quantum-autoencoder algorithm to go beyond the limitations, our model can achieve high recovering fidelity for general input states. Appropriate noise channels are used to make the input mixedness and output mixedness consistent, the noise setup is determined by measurement results of the trash system. Compared with the original quantum-autoencoder model, the measurement information is fully used in our algorithm. In addition to the circuit model, we design a (noise-assisted) adiabatic model of quantum autoencoder that can be implemented on quantum annealers. We verify the validity of our methods through compressing the thermal states of the transverse-field Ising model and Werner states. For pure-state ensemble compression, we also introduce a projected quantum-autoencoder algorithm.
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.
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.
Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.
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.
We implement a Quantum Autoencoder (QAE) as a quantum circuit capable of correcting Greenberger-Horne-Zeilinger (GHZ) states subject to various noisy quantum channels : the bit-flip channel and the more general quantum depolarizing channel. The QAE shows particularly interesting results, as it enables to perform an almost perfect reconstruction of noisy states, but can also, more surprisingly, act as a generative model to create noise-free GHZ states. Finally, we detail a useful application of QAEs : Quantum Secret Sharing (QSS). We analyze how noise corrupts QSS, causing it to fail, and show how the QAE allows the QSS protocol to succeed even in the presence of noise.