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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 a lack of systematic evidence on how quantum data encoding affects classical machine-learning models. It compares encoding methods empirically and finds that ensemble methods balance enhanced performance with added computational time.
Problem
Method
Results
Ensemble methods balanced enhanced performance against increased computational time, while low-complexity models had modest runtime increases and nonlinear-kernel SVMs had more noticeable increases.
Source: §5 · p. 15Takeaways & Limitations
The comparative findings can inform the selection of encoding strategies for quantum-enhanced machine-learning applications.
Source: §6 · p. 16Because the study did not exhaustively explore all algorithms and encoding techniques, its findings generalize only to the methods investigated.
Source: §5 · pp. 15–16
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 study investigates how classical data can be mapped into quantum states and which encoding techniques are promising for classical machine learning. It compares representations under consistent dataset conditions to assess their effects and practical implications.
- The study asks how classical data can be translated into quantum representations and which encoding techniques yield promising results for classical machine learning.Source: §1 · p. 2
- It empirically compares basis, angle, and amplitude encoding, examining their effects on machine learning performance across classical and quantum datasets.Source: §1 · p. 2
- Using the same dataset across experiments is intended to make comparisons objective and isolate the effects of encoding techniques.Source: §1 · p. 2
- The research aims to provide practical guidance and nuanced perspectives on using quantum data representations to augment classical data analysis and machine learning.Source: §1 · p. 2
2 Literature Review
The review surveys developments in quantum data encoding and classical machine learning, framing quantum data representation as a promising area for data analysis. It identifies a lack of systematic empirical research on how encoding affects classical ML performance.
- Feynman’s 1982 proposal that quantum systems could efficiently simulate physical systems helped lay the groundwork for quantum data encoding.Source: §2 · p. 2
- Preskill’s introduction of NISQ devices highlighted the possibility that early-stage quantum computers could outperform classical computers in some applications [1].Source: §2 · p. 2
- Michael Brown’s 2021 work explored enhancing classical ML models with quantum data representations and emphasized harnessing quantum systems for data analysis.Source: §2 · p. 2
- Because systematic studies of encoding effects on classical ML are scarce, this paper compares encoding methods empirically to assess their impact on model performance.The review presents this study as addressing the research gap through rigorous experiments and comparative analysis of practical opportunities and challenges.Source: §2 · p. 3
3 Quantum Computing
Quantum computing’s distinctive properties—including superposition, entanglement, and interference—offer potential advantages for specific applications, though universal capabilities remain under exploration.
3 Quantum Computing
- Superposition lets qubits occupy multiple states simultaneously, enabling parallel computations, while quantum parallelism evaluates multiple possibilities concurrently.The passage also describes entanglement as linking qubit states across distance and interference as using probability amplitudes to enhance computational efficiency.Source: §3 · p. 3
- Quantum tunneling can overcome classical barriers, and Shor’s and Grover’s algorithms promise exponential speedup for specific problems.The passage cites quantum tunneling and Shor’s and Grover’s algorithms [12][13].Source: §3 · p. 3
- The no-cloning theorem prohibits perfect cloning of an unknown quantum state, while error-correction codes help maintain computation reliability.The passage identifies the no-cloning theorem as supporting quantum-cryptography security and error-correction codes as crucial for reliability [14].Source: §3 · p. 3
4 Quantum Data
Quantum data is represented and processed through qubits, states, registers, and circuits. The section describes several ways to map classical information into quantum states, including basis, superposition, angle, and amplitude encoding.
4 Quantum Data
- Quantum data uses qubits represented as states, registers, or circuits; superposition allows multiple states, and entanglement correlates qubits.Quantum gates manipulate and transform quantum states.Source: §4 · pp. 3–4
4.1.1 Basis Encoding (or Computational Basis Encoding)
- Basis encoding maps classical bits directly to computational-basis qubits, representing binary or integer data as states such as |101⟩.For text, each ASCII character can be converted to binary and encoded as a qubit string.Source: §4.1.1 · p. 5
4.1.2 Superposition Encoding
- Superposition encoding represents information as a linear combination of basis states, allowing qubits to encode multiple possibilities simultaneously.Source: §4.1.2 · p. 5
4.1.3 Angle Encoding
- Angle encoding integrates classical information into quantum states through rotation angles, using gates such as Rx or Ry and rotations around arbitrary axes.An optional phase factor depends on the encoding scheme.Source: §4.1.3 · pp. 5–6
4.1.4 Amplitude Encoding
- Amplitude encoding stores classical information in quantum-state amplitudes; the squared magnitude of an amplitude determines the probability of measuring its outcome.Source: §4.1.4 · p. 7
5 Experimental Results
Quantum data embedding generally matched or improved classification performance over PCA encoding, with Quantum Basis Encoding showing competitive or superior results across the tested models. Its runtime cost varied by algorithm, while ensemble methods showed a favorable performance–overhead balance.
5 Experimental Results
- The experiment compared three quantum encodings with PCA across classification models using an 80:20 train-test split and accuracy, precision, sensitivity/recall, F1, and ROC AUC metrics.The telecommunications churn dataset contained 7,043 customers; simulator limits led to majority-class undersampling, leaving 3,738 records.Source: §5 · pp. 7, 8, 15
- Quantum Basis Encoding was competitive or superior to PCA, with accuracy and F1 improvements reported across several classifiers.Logistic Regression, KNN, and Decision Tree improved in accuracy and precision; ensemble models showed noteworthy accuracy and F1 gains. Table 1 compares classical and quantum embedding, but the supplied passages do not provide its cell values.Source: §5 · pp. 8, 15, Table 1 · p. 9
- SVM responses varied by kernel: the linear kernel benefited significantly from quantum encoding, while polynomial and RBF kernels showed varying improvement.The reported runtime increase was more noticeable for SVMs using non-linear kernels.Source: §5 · p. 15
- Quantum encoding modestly increased runtime for Logistic Regression and KNN, while ensemble methods balanced performance gains against overhead without prohibitively long runtimes.The authors suggest accuracy and F1 gains may justify the modest added computational cost for some applications.Source: §5 · p. 15
- Findings are limited to the methods and dataset studied, and may vary with dataset characteristics, hardware, quantum noise, and error rates.The paper recommends optimizing encoding overhead and investigating scalability for practical applications.Source: §5 · pp. 15–16
6 Conclusion
The study compares basis, angle, and amplitude encoding to clarify how classical-to-quantum data mapping relates to machine learning performance. Its findings provide a foundation for selecting encoding strategies in quantum-enhanced applications.
6 Conclusion
- The comparative analysis examines basis, angle, and amplitude encoding, identifying distinct advantages and limitations across the methods.The study frames these differences as relevant to understanding encoding choices for machine learning.Source: §6 · p. 16
- The research provides a foundation for understanding the nuanced relationship between quantum data encoding and machine learning performance.Source: §6 · p. 16
- These insights can inform the selection of encoding strategies for quantum-enhanced machine learning applications as the field evolves.Source: §6 · p. 16
Corresponding Authors
The paper identifies Minati Rath and Hema Date as the contacts for correspondence.
Corresponding Authors
- Correspondence is to Minati Rath or Hema Date.Source: Corresponding Authors · p. 18