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Quantum Data Encoding: A Comparative Analysis of Classical-to-Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy
Minati Rath, Hema Date
TL;DR
The paper addresses limited systematic evidence on how quantum data encoding affects classical machine-learning models. It empirically compares basis, angle, and amplitude encoding across multiple algorithms and evaluation measures, finding performance gains alongside algorithm-dependent computational overhead. Ensemble methods show a relatively balanced relationship between improved performance and added running time, while the findings remain bounded by the studied methods, datasets, hardware, and metrics.
Problem
Systematic evidence remains limited on the effectiveness of quantum data encoding for enhancing classical machine-learning models.
Method
The study empirically compares basis, angle, and amplitude encoding across classical machine-learning algorithms using classification metrics and consistent data representations.
Results
Quantum data embedding improved classification accuracy and F1 scores, while running-time effects varied by algorithm; ensemble methods offered a more balanced performance–overhead trade-off.
Takeaways & Limitations
Quantum data encoding may enhance classical machine-learning performance, but its practical value should be weighed against computational overhead.
Takeaways & Limitations
Generalizability is limited by the specific algorithms and encoding techniques studied, dataset and hardware characteristics, selected metrics and PCA dimensions, and assumptions about reliable scalable quantum hardware.
Abstract
from arXiv · showhide
This research explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms, aiming to assess the performance enhancements and computational implications across a spectrum of models. We explore various classical-to-quantum mapping methods, ranging from basis encoding, 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 in enhancing classical ML models and emphasizes the importance of weighing performance improvements against computational costs. Future research directions may involve refining quantum encoding processes to optimize computational efficiency and exploring scalability for real-world applications. Our work contributes to the growing body of knowledge at 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.
1 Introduction
The paper examines how classical data can be translated into quantum representations and how different encoding methods affect classical machine-learning performance. It uses consistent datasets and comparative experimentation to assess practical implications.
- The study asks how classical data can be effectively translated into quantum representations and which encoding techniques best support classical machine-learning models.
- It empirically evaluates basis, angle, and amplitude encoding across classical and quantum datasets.
- Using the same dataset across experiments helps isolate the effects of encoding techniques on machine-learning performance.
- The research aims to provide practical insights into quantum data encoding for classical machine learning through systematic experimentation and comparative analysis.
- The study frames quantum data encoding as an area with both opportunities and challenges at the intersection of classical and quantum computing.
2 Literature Review
The literature connects quantum computing, quantum data encoding, and classical machine learning, but systematic evidence on encoding effectiveness remains limited. This paper addresses that gap through empirical comparison of encoding methods and their effects on classical-machine-learning performance.
- Quantum data encoding provides a route for translating classical data into quantum representations within the broader development of quantum computing.
- Prior work highlights the potential of quantum systems and quantum data representations to advance classical data analysis.
- A notable research gap is the lack of systematic investigation into whether quantum data encoding enhances classical machine-learning models.
- Comprehensive empirical studies of the practical implications of quantum data encoding for classical machine learning remain relatively scarce.
3 Quantum Computing
Quantum computing differs from classical computing through properties such as superposition and entanglement. These properties provide the conceptual basis for quantum information processing and potential distributed computation.
- Superposition allows qubits to exist in multiple states simultaneously, enabling parallel computations.
- Entanglement links the states of qubits across separation and offers potential for distributed quantum computing.
4 Quantum Data
Quantum data encompasses quantum states, registers, gates, measurements, and entangled states, while encoding techniques translate classical information into quantum representations. The section describes basis, superposition, angle, and amplitude-based approaches and their associated operations.
- Quantum Data: Quantum data is information stored and processed with qubits, quantum states, registers, or circuits, governed by quantum-mechanical principles.Unlike binary classical data, quantum data can exploit superposition and entanglement.
- Basis Encoding: Basis encoding directly maps classical bits to computational-basis qubits, so a classical value such as 101 becomes the state |101⟩.ASCII characters can likewise be converted to binary representations and encoded as qubit states.
- Superposition Encoding: Superposition encoding represents information as a linear combination of basis states, allowing multiple classical possibilities to be encoded simultaneously.The representation relies on placing qubits in superpositions of classical states.
- Angle Encoding: Angle encoding represents classical information through qubit rotations, with gates such as Ry or Rx applying angles associated with the input values.The rotation may use an arbitrary axis on the Bloch sphere, and the phase factor can be optional depending on the scheme.
- Amplitude Encoding: Amplitude encoding stores classical information in the amplitudes of a quantum superposition, with measurement probabilities determined by squared amplitudes.The input terms are square-normalized before being used in the quantum state.
5 Experimental Results
The experiment evaluated classical and quantum data representations across several machine-learning algorithms, using an 80:20 train-test split and multiple classification metrics. Quantum embedding generally improved ensemble-model performance, while its runtime cost varied by algorithm complexity.
- Experimental setup: PCA dimensionality reduction identified an elbow point at 23 components, with cumulative explained variance of 1.0000000000000002.The reported explained variance ratio at the elbow point was 8.126234391114803e-33.
- Evaluation: Performance was compared using accuracy, precision, sensitivity, recall, F1 score, and ROC AUC across classical PCA and quantum-encoded data.The experiment used an 80:20 train-test split for the classical and quantum embedding comparison.
- Performance results: Quantum Basis Encoding produced competitive or superior results compared with PCA across the evaluated classical machine-learning models.The study compared Quantum Basis, Quantum Angle, and Quantum Amplitude Encoding with PCA-based classical representations.
- Runtime results: Quantum encoding caused modest runtime increases for Logistic Regression and KNN but more noticeable increases for SVM, especially with non-linear kernels.The added computational overhead varied with algorithm complexity and kernel choice.
- Performance results: Random Forest, LightGBM, AdaBoost, and CatBoost showed improvements in accuracy and F1 score with quantum data embedding.These ensemble methods exhibited a more balanced relationship between performance gains and additional computation.
- Limitations: The study did not exhaustively evaluate all machine-learning algorithms or quantum encoding techniques, limiting generalizability to the methods investigated.Results may also vary with dataset characteristics, hardware, PCA dimensions, noise, and quantum-processor error rates.
6 Conclusion
The conclusion frames the study as a comparative investigation of classical-to-quantum data-mapping techniques and their effects on machine-learning accuracy. It emphasizes that the findings support more informed selection of encoding strategies as quantum-enhanced machine learning develops.
- Conclusion: The study compared basis, angle, and amplitude encoding to clarify their distinct advantages and limitations for machine-learning performance.The conclusion presents this comparison as a foundation for understanding the relationship between quantum data encoding and machine learning.
Author Information
The paper identifies Minati Rath and Hema Date as authors affiliated with the Faculty of Decision Science at IIM Mumbai, India.
- Author Information: Minati Rath and Hema Date are affiliated with the Faculty of Decision Science, IIM Mumbai, India.
Corresponding Authors
Correspondence for the paper is directed to Minati Rath or Hema Date.
- Corresponding Authors: The paper lists Minati Rath or Hema Date as correspondence contacts.