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arXiv:2404.08429 · Chinese Physics Letters

Optimized Quantum Autoencoder

Yibin Huang, Muchun Yang, D. L. Zhou

Published Jan 5, 2026• 2 citations
arXivHTMLPDF

Abstract

Abstract Quantum autoencoder (QAE) compresses a bipartite quantum state into its subsystem using a self-checking mechanism. How to characterize and minimize the lost information in this process is essential for understanding the compression mechanism of QAE. Here, we investigate how to minimize the lost information in QAE for any input mixed state. We theoretically show that the lost information is the quantum mutual information between the remaining subsystem and the discarded one; the encoding unitary transformation is designed to minimize this mutual information. Furthermore, we show that the optimized unitary transformation can be decomposed as the product of a permutation unitary transformation and a disentanglement unitary transformation, and the permutation unitary transformation can be searched by a regular Young tableau algorithm. When the search can be made exhaustive in lower-dimensional systems, the lost information is minimized numerically, which is shown theoretically to be a global minimum. When the dimension of the system becomes larger such that an exhaustive search is impossible, we adopt an approximate search algorithm to numerically identify that our compression scheme gives lower lost information than that from the quantum variational circuit-based QAE.

DOI
10.1088/0256-307x/43/2/020601

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Abstract Quantum autoencoder (QAE) compresses a bipartite quantum state into its subsystem using a self-checking mechanism. How to characterize and minimize the lost information in this process is essential for understanding the compression mechanism of QAE. Here, we investigate how to minimize the lost information in QAE for any input mixed state. We theoretically show that the lost information is the quantum mutual information between the remaining subsystem and the discarded one; the encoding unitary transformation is designed to minimize this mutual information. Furthermore, we show that the optimized unitary transformation can be decomposed as the product of a permutation unitary transformation and a disentanglement unitary transformation, and the permutation unitary transformation can be searched by a regular Young tableau algorithm. When the search can be made exhaustive in lower-dimensional systems, the lost information is minimized numerically, which is shown theoretically to be a global minimum. When the dimension of the system becomes larger such that an exhaustive search is impossible, we adopt an approximate search algorithm to numerically identify that our compression scheme gives lower lost information than that from the quantum variational circuit-based QAE.
A quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology. In this work, generalizing the ideas of classical and quantum autoencoders, we introduce the quantum circuit autoencoder (QCAE) model to compress and encode information within quantum circuits. We provide a comprehensive protocol for QCAE and design a variational quantum algorithm, varQCAE, for its implementation. We theoretically analyze this model by deriving conditions for lossless compression and establishing both upper and lower bounds on its recovery fidelity. Finally, we apply varQCAE to three practical tasks, and numerical results show that it can effectively (1) compress the information within quantum circuits, (2) detect anomalies in quantum circuits, and (3) mitigate the depolarizing noise in quantum circuits. These suggest that our algorithm is potentially applicable to other information processing tasks for quantum circuits.
Abstract We present the enhanced feature quantum autoencoder, or EF-QAE, a variational quantum algorithm capable of compressing quantum states of different models with higher fidelity. The key idea of the algorithm is to define a parameterized quantum circuit that depends upon adjustable parameters and a feature vector that characterizes such a model. We assess the validity of the method in simulations by compressing ground states of the Ising model and classical handwritten digits. The results show that EF-QAE improves the performance compared to the standard quantum autoencoder using the same amount of quantum resources, but at the expense of additional classical optimization. Therefore, EF-QAE makes the task of compressing quantum information better suited to be implemented in near-term quantum devices.
Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a kkk-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure nnn-qubit states, there exists a QAE with kkk encoder ancillas and nnn decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least kkk encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.
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 One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a reference state. When taking a pure reference state, there exists an upper bound for the encoding fidelity, which limits the compression of states with high entropy. To overcome the entropy inconsistency, we allow the reference state to be a mixed state and propose a cost function that combines the encoding fidelity and the quantum mutual information. We consider the reference states to be a mixture of maximally mixed states and pure states and propose three strategies for setting the ratio of mixedness. Numerical simulations of different states and experimental implementations on IBM quantum computers illustrate the effectiveness of our approach.
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.