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arXiv:2501.15359 · Physical Review Letters

Neural Quantum Embedding via Deterministic Quantum Computation with One Qubit

Hongfeng Liu, Tak Hur, Shitao Zhang, Liangyu Che, Xinyue Long, Xiangyu Wang, Keyi Huang, Yu-ang Fan, Yuxuan Zheng, Yufang Feng, Yu Zhou, Jack Tsz Fai Ng, Xinfang Nie, Daniel K. Park, Dawei Lu

Published Jul 29, 2025• 5 citations
arXivHTMLPDF

Abstract

Quantum computing is expected to provide an exponential speedup in machine learning. However, optimizing the data loading process, commonly referred to as "quantum data embedding," to maximize classification performance remains a critical challenge. In this Letter, we propose a neural quantum embedding (NQE) technique based on deterministic quantum computation with one qubit (DQC1). Unlike the traditional embedding approach, NQE trains a neural network to maximize the trace distance between quantum states corresponding to different categories of classical data. Furthermore, training is efficiently achieved using DQC1, which is specifically designed for ensemble quantum systems, such as nuclear magnetic resonance (NMR). We validate the NQE-DQC1 protocol by encoding handwritten images into NMR quantum processors, demonstrating a significant improvement in distinguishability compared to traditional methods. Additionally, after training the NQE, we implement a parametrized quantum circuit for classification tasks, achieving 98% classification accuracy, in contrast to the 54% accuracy obtained using traditional embedding. Moreover, we show that the NQE-DQC1 protocol is extendable, enabling the use of the NMR system for NQE training due to its high compatibility with DQC1, while subsequent machine learning tasks can be performed on other physical platforms, such as superconducting circuits. Our Letter opens new avenues for utilizing ensemble quantum systems for efficient classical data embedding into quantum registers.

DOI
10.1103/y8wr-yml4

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Quantum computing is expected to provide an exponential speedup in machine learning. However, optimizing the data loading process, commonly referred to as "quantum data embedding," to maximize classification performance remains a critical challenge. In this Letter, we propose a neural quantum embedding (NQE) technique based on deterministic quantum computation with one qubit (DQC1). Unlike the traditional embedding approach, NQE trains a neural network to maximize the trace distance between quantum states corresponding to different categories of classical data. Furthermore, training is efficiently achieved using DQC1, which is specifically designed for ensemble quantum systems, such as nuclear magnetic resonance (NMR). We validate the NQE-DQC1 protocol by encoding handwritten images into NMR quantum processors, demonstrating a significant improvement in distinguishability compared to traditional methods. Additionally, after training the NQE, we implement a parametrized quantum circuit for classification tasks, achieving 98% classification accuracy, in contrast to the 54% accuracy obtained using traditional embedding. Moreover, we show that the NQE-DQC1 protocol is extendable, enabling the use of the NMR system for NQE training due to its high compatibility with DQC1, while subsequent machine learning tasks can be performed on other physical platforms, such as superconducting circuits. Our Letter opens new avenues for utilizing ensemble quantum systems for efficient classical data embedding into quantum registers.
Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data and has substantial impacts on performance outcomes. In this study, we present neural quantum embedding (NQE), a method that efficiently optimizes quantum embedding beyond the limitations of positive and trace-preserving maps by leveraging classical deep-learning techniques. NQE enhances the lower bound of the empirical risk, leading to substantial improvements in classification performance. Moreover, NQE improves robustness against noise. To validate the effectiveness of NQE, we conduct experiments on IBM quantum devices for image data classification, resulting in a remarkable accuracy enhancement from 0.52 to 0.96. In addition, numerical analyses highlight that NQE simultaneously improves the trainability and generalization performance of quantum neural networks, as well as of the quantum kernel method.
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
Abstract Hybrid quantum–classical models for text classification are constrained by the mismatch between high-dimensional sentence embeddings and the limited number of qubits available in Noisy Intermediate-Scale Quantum (NISQ) hardware. Existing approaches rely on fixed dimensionality-reduction techniques such as PCA, which compress embeddings independently of the learning task and often remove semantic information essential for downstream classification. This work addresses this limitation by applying Neural Quantum Embedding (NQE) to sentence-level sentiment analysis. NQE jointly performs nonlinear neural compression and quantum-oriented encoding, producing compact embeddings optimized for variational circuits.We integrate NQE with a Quantum Neural Network based on a three-layer SU(4) ansatz. Experiments on three sentence-level sentiment datasets show that NQE substantially improves hybrid quantum performance, increasing accuracy by up to 38%, with corresponding improvements in precision, recall, and F1-score. Additional experiments with a classical neural network demonstrate that NQE also enhances classical performance, yielding accuracy gains of up to 6.3%. Although classical models achieve higher absolute accuracy due to greater representational capacity, the relative improvement introduced by NQE is significantly larger in the quantum setting, where embedding structure must align with strict hardware constraints.Overall, this study introduces a task-adaptive, learnable embedding mechanism that bridges the representational gap between classical embeddings and quantum circuits. The results show that NQE improves optimization stability, enhances quantum-state separability, and enables more effective hybrid sentiment classification within NISQ limitations
The rapid emergence of quantum technology has raised new challenges in distinguishing various quantum circuits of similar functions. In this work, we propose parallel quantum embedding neural network (ParaQuanNet) for the efficient identification of quantum generative circuits via classifications of the corresponding output data. Specifically, we generated W-like states with eight generative quantum circuits realizing the generative quantum denoising diffusion probabilistic models (QDDPM). Our ParaQuanNet can classify these eight classes of generated quantum data with an accuracy of {99.5%99.5\%99.5%}, even though all of them are trained to generate the same types of quantum data. With a novel design of parallel quantum embedding unit (PQEU) in our neural networks, our ParaQuanNet enables the quantum kernel circuit parallelly process all the receptive fields of quantum data, which empowers the quantum data processing efficiency. We also integrate the mutually unbiased measurements into our ParaQuanNet and further improve its performance. We apply our ParaQuanNet on the classification of classical data sets and demonstrate a good performance of quantum neural networks on these tasks. Our approach demonstrates good robustness to noisy data and the circuit-level noise with a Python realization in a classical GPU. Our results highlight ParaQuanNet as a scalable and effective framework for quantum circuits identification, contributing to the broader development of quantum machine intelligence.
Tremendous progress has been witnessed in artificial intelligence within the domain of neural network backed deep learning systems and its applications. As we approach the post Moore’s Law era, the limit of semiconductor fabrication technology along with a rapid increase in data generation rates have lead to an impending growing challenge of tackling newer and more modern machine learning problems. In parallel, quantum computing has exhibited rapid development in recent years. Due to the potential of a quantum speedup, quantum based learning applications have become an area of significant interest, in hopes that we can leverage quantum systems to solve classical problems. In this work, we propose a quantum deep learning architecture; we demonstrate our quantum neural network architecture on tasks ranging from binary and multi-class classification to generative modelling. Powered by a modified quantum differentiation function along with a hybrid quantum-classic design, our architecture encodes the data with a reduced number of qubits and generates a quantum circuit, loading it onto a quantum platform where the model learns the optimal states iteratively. We conduct intensive experiments on both the local computing environment and IBM-Q quantum platform. The evaluation results demonstrate that our architecture is able to outperform Tensorflow-Quantum by up to 12.51% and 11.71% for a comparable classic deep neural network on the task of classification trained with the same network settings. Furthermore, our GAN architecture runs the discriminator and the generator purely on quantum hardware and utilizes the swap test on qubits to calculate the values of loss functions. In comparing our quantum GAN, we note our architecture is able to achieve similar performance with 98.5% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms other quantum based GANs in the literature for up to 125.0% in terms of similarity between generated distributions and original data sets.
Image classification is a core task in the field of computer vision, with significant implications for applications such as medical imaging and autonomous driving. Classical neural network architectures face numerous challenges when dealing with high-dimensional and complex data, particularly in terms of feature extraction and data processing capabilities, limiting their performance in certain applications. Quantum computing offers promising new approaches to processing high-dimensional complex data, most notably through Parameterized Quantum Circuits (PQC) as quantum hybrid neural networks for image classification. In this paper, we propose a hybrid neural network featuring a specific PQC structure designed to generate entanglement in accordance with sample images. This PQC structure utilizes the adjacency matrix of the corresponding graph of the sample image, embedding adjacency relationships among nodes into the entanglement module, thereby generating entanglement aligned with the features of specific images. Numerical results validate the effectiveness of our PQC model across various image classification tasks, enhancing the efficiency of feature learning and representation. Our model demonstrates significant advantages in classification accuracy and learning efficiency on classical datasets. Our research not only advances the theoretical understanding of hybrid quantum networks but also paves the way for practical implementations in real-world scenarios.