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arXiv:2508.00768 · Advanced Quantum Technologies

Evaluating Angle and Amplitude Encoding Strategies for Variational Quantum Machine Learning: Their Impact on Model's Accuracy

Antonio Tudisco, Andrea Marchesin, Maurizio Zamboni, Mariagrazia Graziano, Giovanna Turvani

Published Apr 1, 2026• 8 citations
arXivHTMLPDF

Abstract

ABSTRACT Recent advancements in Quantum Computing and Machine Learning have increased attention to Quantum Machine Learning (QML), which aims to develop machine learning models by exploiting the quantum computing paradigm. One of the widely used models in this area is the Variational Quantum Circuit (VQC), a hybrid model where the quantum circuit handles data inference while classical optimization adjusts the parameters of the circuit. The quantum circuit consists of an encoding layer, which loads data into the circuit, and a template circuit, known as the ansatz, responsible for processing the data. This work involves performing an analysis by considering both Amplitude‐ and Angle‐encoding models, and examining how the type of rotational gate applied affects the classification performance of the model. This comparison is carried out by training the different models on two datasets, Wine and Diabetes, and evaluating their performance. The study demonstrates that, under identical model topologies, the difference in accuracy between the best and worst models ranges from 10% to 30%, with differences reaching up to 41%. Moreover, the results highlight how the choice of rotational gates used in encoding can significantly impact the model's classification performance. The findings confirm that the embedding represents a hyperparameter for VQC models.

DOI
10.1002/qute.202500611

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ABSTRACT Recent advancements in Quantum Computing and Machine Learning have increased attention to Quantum Machine Learning (QML), which aims to develop machine learning models by exploiting the quantum computing paradigm. One of the widely used models in this area is the Variational Quantum Circuit (VQC), a hybrid model where the quantum circuit handles data inference while classical optimization adjusts the parameters of the circuit. The quantum circuit consists of an encoding layer, which loads data into the circuit, and a template circuit, known as the ansatz, responsible for processing the data. This work involves performing an analysis by considering both Amplitude‐ and Angle‐encoding models, and examining how the type of rotational gate applied affects the classification performance of the model. This comparison is carried out by training the different models on two datasets, Wine and Diabetes, and evaluating their performance. The study demonstrates that, under identical model topologies, the difference in accuracy between the best and worst models ranges from 10% to 30%, with differences reaching up to 41%. Moreover, the results highlight how the choice of rotational gates used in encoding can significantly impact the model's classification performance. The findings confirm that the embedding represents a hyperparameter for VQC models.
We investigate two fundamental data encoding strategies for gate-based quantum computers: amplitude encoding and angle encoding. In amplitude encoding, a normalized -dimensional classical vector is mapped into the probability amplitudes of a -qubit quantum state, whereas angle encoding uses one or more single-qubit rotation gates per feature to encode data as angles.[1, 2] We construct a toy binary classification dataset with four real-valued features and compare these encoding schemes using a variational quantum classifier (VQC) approach. Our results indicate that angle encoding often yields slightly higher classification accuracy (e.g. 82% vs. 75% in one experiment) at the cost of requiring more qubits, while amplitude encoding compresses features into fewer qubits (2 vs. 4) but demands deeper state-preparation circuits. These findings align with previous studies that report higher accuracy for rotation encodings (e.g. vs. in MNIST experiments [3]) and note that the encoding choice acts as a hyperparameter affecting VQC performance. [4]
Nowadays, quantum-enhanced methods have been widely studied to solve machine learning related problems. This article presents the application of a Variational Quantum Classifier (VQC) for binary classification. We utilized three datasets: a synthetic dataset with randomly generated values between 0 and 1, the publicly available University of California Intelligence Machine learning (UCI) sonar dataset consisting of mining data, and a proprietary diabetes dataset related to diabetes with acute diseases and diabetes without acute disease. To deal with the limitation of noisy intermediate-scale quantum systems (NISQ), we used a pre-processing method to enhance the prediction rate when applying the VQC method. The process includes feature selection and state preparation. Quantum state preparation is critical for obtaining a functioning pipeline in a quantum machine learning (QML) model. Amplitude encoding is a state preparation approach that enhances the performance of data encoding and the learning of quantum models. As a result, our proposed methods achieved accuracies of 75%, 71.4%, and 68.73% by using VQC model and in contrast, the amplitude encoding-based VQC achieved 98.40%, 67.3%, and 74.50% accuracies on the synthetic, sonar, and diabetes dataset, respectively.
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.
Quantum Computing (QC) is an emerging paradigm offering fundamentally a new and more effective way of computation based on the properties of quantum mechanics, such as superposition, entanglement, and quantum parallelism. The intersection of QC and Machine Learning (ML) fields has given rise to a new research area, Quantum Machine Learning (QML). With the computational power of quantum computers, it proposes using quantum computers to process classical data for learning. Therefore, QML can be an efficient means of classification for computationally intensive tasks. In this paper, we perform an experimental binary classification task with our three qubit Ansatz/Variational Quantum Circuit (VQC). The dataset used in this study, Maternal Health Risk Data Set (MHRD), is publicly available and collected from different hospitals and clinics by means of Internet of Things (IoT) systems. We use amplitude embedding to encode feature vector to the state of qubits after preprocessing and normalization of the data. The operations of cost value calculation and parameter tuning are carried out in a classical way. We have tested our proposal with PennyLane library, and the experimental results show that the proposed VQC classifies the data with 92% accuracy.
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical machine learning. This article suggests a broad architecture that allows the connection between classical data pipelines and quantum algorithms, hybrid quantum-classical models emerge as a promising route to scalable and near-term quantum benefit. At the core of this paradigm lies the Classical-Quantum (CQ) paradigm, in which the qubit states of high-dimensional classical data are encoded using sophisticated classical encoding strategies which encode the data in terms of amplitude and angle of rotation, along with superposition mapping. These techniques allow compression of information exponentially into Hilbert space representations, which, together with reduced sample complexity, allows greater feature expressivity. We also examine variational quantum circuits, quantum gates expressed as trainable variables that run with classical optimizers to overcome decoherence, noise, and gate-depth constraints of the existing Noisy Intermediate-Scale Quantum (NISQ) devices. Experimental comparisons with a Quantum Naive Bayes classifier prove that even small quantum circuits can approximate probabilistic inference with competitive accuracy compared to classical benchmarks, and have much better robustness to noisy data distributionsThis model does not only explain the algorithmic and architectural design of QML, it also offers a roadmap to the implementation of quantum kernels, variational algorithms, and hybrid feedback loops into practice, including optimization, computer vision, and medical diagnostics. The results support the idea that hybrid architectures with strong data encoding and adaptive error protection are key to moving QML out of theory to practice.
Quantum Machine Learning methods are becoming a key component for various types of tasks making predictions or decisions based on datasets. Recent efforts and researches on quantum computing point out the significance of quantum speedup advantage, especially for learning processes that require enormous amount of computational resources. Advances in both quantum hardware design and hybrid quantum-classical software frameworks accommodate a paradigm shift from classical to quantum. In consideration with this quantum leap notion, we investigate the capability of variational quantum algorithms (VQA) on a real world problem of user localization dealing with the binary classification task. This paper introduces a VQA with four variants that differ in the number of layers related to the variational quantum circuit (VQC) part of the VQA. The samples from a publicly available user localization dataset are first preprocessed through padding, scaling and normalization. Next, they are mapped into three qubit quantum states using amplitude encoding as a data embedding scheme. Unitary transformation of the mapped quantum data in the VQC is followed by a measurement in computational basis to produce predictions for the labels. The error between true and predicted labels is computed in a classical manner and a cost function minimization process is executed with the aid of gradient descent algorithm. The updated training parameters from the optimization stage are fed into the VQC and this process is repeated until the learnable parameters converge. The simulation results demonstrate that the designed VQA for binary classification achieves an accuracy value of 99% in the training phase. Moreover, the ratio of predicted labels to true labels approaches to 93% during the validation of actual user locations based on the signal strength received from the routers that are positioned at different places in a facility. Keywords—quantum machine learning, user localization, variational quantum algorithm, variational quantum circuit, amplitude encoding