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.
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.
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
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.
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.
We investigate the application of Neural Quantum Embedding and Quantum Neural Networks for sentiment analysis using the Stanford Sentiment Treebank dataset. We adapt the Neural Quantum Embedding framework, originally worked with image classification, to textual data by employing quantum embedding techniques that maximize trace distance for better data separability. Additionally, we incorporate advanced quantum feature maps and preprocessing techniques from recent quantum machine learning studies to enhance classification performance. Our experimental results demonstrate that the quantum models catch up with the classical baselines in sentiment classification accuracy, particularly in noisy intermediate-scale quantum settings. This work highlights the feasibility and potential of quantum-assisted sentiment analysis.
This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.
This study explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms; to assess performance enhancements and computational implications across a spectrum of models. We explored various classical-to-quantum mapping methods; ranging from basis encoding and angle encoding to amplitude encoding; for encoding classical data. We conducted an extensive empirical study encompassing popular ML algorithms, including Logistic Regression, K-Nearest Neighbors, Support Vector Machines, and ensemble methods like Random Forest, LightGBM, AdaBoost, and CatBoost. Our findings reveal that quantum data embedding contributes to improved classification accuracy and F1 scores, particularly notable in models that inherently benefit from enhanced feature representation. We observed nuanced effects on running time, with low-complexity models exhibiting moderate increases and more computationally intensive models experiencing discernible changes. Notably, ensemble methods demonstrated a favorable balance between performance gains and computational overhead. This study underscores the potential of quantum data embedding to enhance classical ML models and emphasizes the importance of weighing performance improvements against computational costs. Future research may involve refining quantum encoding processes to optimize computational efficiency and explore scalability for real-world applications. Our work contributes to the growing body of knowledge on the intersection of quantum computing and classical machine learning, offering insights for researchers and practitioners seeking to harness the advantages of quantum-inspired techniques in practical scenarios.