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Entropy

Autoencoding-Assisted Quantum Cloning Machine

Qian Jun Beh, Moritz Straeter, Zeen Sun, L. C. Kwek, Yuancheng Zhan

Published May 18, 2026• 0 citations
Publisher

Abstract

Quantum cloning machines are essential in quantum information processing, finding applications in areas such as quantum communication and cryptographic protocols. However, the fidelity of universal quantum cloning machines diminishes as the dimension of the Hilbert space increases, resulting in significantly lower efficiency when cloning high-dimensional quantum states compared to qubits. In this study, we introduce a Hybrid Quantum Autocloning Machine (HQAM) that combines quantum autoencoding with universal quantum cloning. The core concept involves compressing a high-dimensional quantum state into a lower-dimensional effective subspace through a quantum autoencoder, conducting the cloning process within this reduced subspace, and then reconstructing the state in the original Hilbert space. Our results show that, for input states with a strong overlap with the effective qubit subspace, the HQAM achieves cloning fidelities exceeding the benchmark fidelity of direct qutrit universal cloning and approaching the optimal qubit cloning limit, while maintaining robustness under noise. These findings demonstrate that compression-assisted cloning provides a practical strategy for improving cloning performance in high-dimensional quantum systems and may enable more efficient quantum information processing protocols.

DOI
10.3390/e28050563

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Quantum cloning machines are essential in quantum information processing, finding applications in areas such as quantum communication and cryptographic protocols. However, the fidelity of universal quantum cloning machines diminishes as the dimension of the Hilbert space increases, resulting in significantly lower efficiency when cloning high-dimensional quantum states compared to qubits. In this study, we introduce a Hybrid Quantum Autocloning Machine (HQAM) that combines quantum autoencoding with universal quantum cloning. The core concept involves compressing a high-dimensional quantum state into a lower-dimensional effective subspace through a quantum autoencoder, conducting the cloning process within this reduced subspace, and then reconstructing the state in the original Hilbert space. Our results show that, for input states with a strong overlap with the effective qubit subspace, the HQAM achieves cloning fidelities exceeding the benchmark fidelity of direct qutrit universal cloning and approaching the optimal qubit cloning limit, while maintaining robustness under noise. These findings demonstrate that compression-assisted cloning provides a practical strategy for improving cloning performance in high-dimensional quantum systems and may enable more efficient quantum information processing protocols.
With quantum resources a precious commodity, their efficient use is highly desirable. Quantum autoencoders have been proposed as a way to reduce quantum memory requirements. Generally, an autoencoder is a device that uses machine learning to compress inputs, that is, to represent the input data in a lower-dimensional space. Here, we experimentally realize a quantum autoencoder, which learns how to compress quantum data using a classical optimization routine. We demonstrate that when the inherent structure of the dataset allows lossless compression, our autoencoder reduces qutrits to qubits with low error levels. We also show that the device is able to perform with minimal prior information about the quantum data or physical system and is robust to perturbations during its optimization routine.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
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.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although such perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signalling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. Here, we perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states, and fully characterize our cloning machine by performing quantum state tomography on \emph{cloned} photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated in order to reveal the robustness of high-dimensional states in quantum cryptography.
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.