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Intelligent Opto-Electronics

Quantum embedding learning on variational photonic quantum circuits

任冠恒, 王东来 Wang Donglai, Lizheng Yan, Yuancheng Zhan, Yiming Ma, Zhanshan Wang, Hui Zhang, Xinbin Cheng

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Quantum embedding is a key technique in quantum machine learning, mapping classical data into a high-dimensional Hilbert space through parameterized quantum circuits to enhance data separability. While effective on general quantum devices, its implementation on photonic platforms faces severe challenges, as entangling gates rely on post-selection and lead to exponentially decreasing success probabilities when cascaded. To address this, we propose a quantum embedding learning approach tailored for photonic quantum circuits, which incorporates multi-photon post-selection into a variational ansatz, enabling the efficient generation of entanglement while maintaining circuit scalability on NISQ devices. By training the transfer matrices, our method achieves the desired photon distribution probabilities and input-output correspondence. We demonstrate its versatility through three tasks: Bell-state projection, quantum support vector machines (qSVM), and quantum clustering of K-means. The experimental results indicate enhanced performance in state discrimination, classification, and clustering, showing that the method provides a practical route to implement quantum embedding in integrated photonic circuits.

DOI
10.67704/ioe.2025.250010

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Quantum embedding is a key technique in quantum machine learning, mapping classical data into a high-dimensional Hilbert space through parameterized quantum circuits to enhance data separability. While effective on general quantum devices, its implementation on photonic platforms faces severe challenges, as entangling gates rely on post-selection and lead to exponentially decreasing success probabilities when cascaded. To address this, we propose a quantum embedding learning approach tailored for photonic quantum circuits, which incorporates multi-photon post-selection into a variational ansatz, enabling the efficient generation of entanglement while maintaining circuit scalability on NISQ devices. By training the transfer matrices, our method achieves the desired photon distribution probabilities and input-output correspondence. We demonstrate its versatility through three tasks: Bell-state projection, quantum support vector machines (qSVM), and quantum clustering of K-means. The experimental results indicate enhanced performance in state discrimination, classification, and clustering, showing that the method provides a practical route to implement quantum embedding in integrated photonic circuits.
Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate-scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques to enhance quantum advantages on NISQ devices. However, most variational algorithms are circuit-model-based and encounter challenges when implemented on integrated photonic circuits, because they involve explicit decomposition of large quantum circuits into sequences of basic entangled gates, leading to an exponential decay of success probability due to the non-deterministic nature of photonic entangling gates. Here, we present a variational learning approach for designing quantum photonic circuits, which directly incorporates post-selection and elementary photonic elements into the training process. The complicated circuit is treated as a single nonlinear logical operator, and a unified design is discovered for it through variational learning. Engineering an integrated photonic chip with automated control, we adjust and optimize the internal parameters of the chip in real time for task-specific cost functions. We utilize a simple case of designing photonic circuits for a single ancilla CNOT gate with improved success rate to illustrate how our proposed approach works, and then apply the approach in the first demonstration of quantum stochastic simulation using integrated photonics.
Abstract Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate‐scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques to enhance quantum advantages on NISQ devices. However, most variational algorithms are circuit‐model‐based and encounter challenges when implemented on integrated photonic circuits, because they involve explicit decomposition of large quantum circuits into sequences of basic entangled gates, leading to an exponential decay of success probability due to the non‐deterministic nature of photonic entangling gates. Here, a variational learning approach is presented for designing quantum photonic circuits, which directly incorporates post‐selection and elementary photonic components into the training process. The complicated circuit is treated as a single nonlinear logical operator and a unified design is discovered for it through variational learning. Engineering an integrated photonic chip with automated control achieved by genetic algorithm, the internal parameters of the chip are adjusted and optimized in real‐time for task‐specific cost functions. A simple case of designing photonic circuits for a single ancilla CNOT gate with improved success rate is utilized to illustrate how the proposed approach works, and then the approach is applied to the first demonstration of quantum stochastic simulation using integrated photonics.
Machine learning models achieve strong predictive performance by uncovering hidden patterns and structures within data. Quantum Machine Learning (QML) extends this capability by leveraging principles of quantum mechanics to address complex classification tasks. However, designing effective feature extraction strategies remains challenging. The choice of ansatz plays a central role in determining the expressive power and learning capability of quantum models. In this work, we propose a parameterized quantum circuit model incorporating adaptive transformations between neighboring qubits to enhance feature extraction and classification performance. The proposed approach is evaluated on seven benchmark datasets from the UCI repository: Iris, Banknote Authentication (BNA), Raisin, Wireless Indoor Localization (WIL), Wine, Penguin, and HTRU2. Its performance is compared against existing quantum classification models, including the Amplitude Embedding Model (AEM), Variational Quantum Circuit (VQC), and Quantum Multi-Class Classifier (QMCC), using identical numbers of layers and training epochs. Additionally, comparisons are made with well-established standard classical classifiers. Experimental results implemented on the PennyLane platform demonstrate that the proposed model achieves high test accuracies within only 10–15 training epochs, reaching 100% (Iris), 98.3% (BNA), 91.1% (Raisin), 97.0% (WIL), 99.2% (Penguin), 94.0% (Wine), and 95.4% (HTRU2). These findings indicate that the proposed ansatz effectively extracts meaningful features and performs competitively in both binary and multi-class classification tasks, highlighting its potential for practical quantum machine learning applications.
The expressivity and scalability of fixed feature embeddings and shallow quantum circuits for Quantum Support Vector Machines (QSVMs) are restricted due to the limitations of near-term hardware. In this work, we propose a novel QSVM framework consisting of Low-Rank Adaptation (LoRA)-modified VisionTransformer embeddings as well as trainable variational quantum circuits. The architecture enhances the representational power by the joint optimization of embedding and circuit parameters. Empirical evaluation on distilled benchmark datasets shows significant performance gains, with up to 38.7% absolute accuracy improvement on MNIST (61.3% to 100.0%). The model also achieves 91% to 100% test accuracies on Fashion-MNIST, KMNIST and CIFAR-10 datasets with only 200 training samples for each dataset. The results show that the performance improvements are due to the joint design between the feature embeddings and the quantum circuits, rather than just the quantum kernels. Cross-dataset evaluations and circuit-depth analyses provide experimental evidence that the approach is suitable for scalable quantum machine learning in image classification tasks.
Abstract Support vector machines (SVMs) are widely used for classification, but become computationally expensive as datasets grow and data become high-dimensional or nonlinearly separable. Quantum support vector machines (QSVMs) enhance the traditional SVMs by replacing conventional feature mappings with quantum-implemented embeddings that project data into high-dimensional Hilbert spaces, potentially improving expressive power and efficiency. However, training QSVMs on current noisy intermediate-scale quantum (NISQ) devices remains challenging, as constructing the quantum kernel matrix requires repeated circuit executions and scales quadratically with dataset size. We propose NQ-SVM , a hybrid quantum-classical method that incorporates the Nystr\"om approximation to enhance the scalability of QSVMs. By selecting a small set of landmark points, the Nystr\"om method yields a low-rank kernel approximation, reducing complexity from (O(n2))(O(n^2))(O(n2)) to (O(nm))(O(nm))(O(nm)), while preserving the quantum advantages in handling high-dimensional, non-linear data. Extensive simulations demonstrate that NQ-SVM achieves comparable classification accuracy to classical SVMs and full QSVMs, while substantially reducing training time and kernel evaluation costs. These results underscore the potential of NQ-SVM as a scalable and practical hybrid framework for near-term quantum machine learning (QML).
Quantum Machine Learning (QML) has emerged as a promising paradigm that combines principles of quantum computation with classical learning techniques to address challenges posed by complex, high-dimensional, and non-linear datasets. This work presents a systematic experimental study of quantum-enhanced classification and clustering using hybrid quantum–classical models evaluated on synthetically generated datasets. Quantum Support Vector Machines (QSVM) and Variational Quantum Classifiers (VQC) are implemented using the Qiskit framework and benchmarked against established classical algorithms. The synthetic datasets are carefully designed to control linearity, dimensionality, class overlap, and nonlinear structure, enabling a detailed performance comparison under both ideal and noisy simulation conditions. The experimental results indicate that quantum feature representations can enhance class separability in non-linear scenarios, while also highlighting the practical limitations imposed by noise sensitivity and circuit depth constraints inherent to Noisy Intermediate-Scale Quantum (NISQ) devices .