Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Benchmarking quantum machine learning kernel training for classification tasks

Diego Alvarez-Estevez

TL;DR

This study benchmarks quantum kernel methods for classification by evaluating Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) on two quantum feature maps, ZZFeatureMap and CovariantFeatureMap, across ad-hoc and standard datasets with classical baselines (SVM and Logistic Regression). QKE embeds data into a quantum feature space and computes kernel entries via state overlaps, while QKT optimizes the embedding parameters θ through a kernel-target-alignment objective, potentially using SPSA. Results show quantum methods outperform classical baselines on ad-hoc datasets but yield mixed performance on broader benchmarks, with QKT offering limited consistent gains relative to its computational cost. The findings underscore the importance of selecting an appropriate quantum feature map and tuning hyperparameters, suggesting that hyperparameter optimization may often be more impactful than QKT training in near-term quantum settings.

Abstract

Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically-crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) in connection with two quantum feature mappings, namely ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad-hoc datasets. In this study, we aim to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically Support Vector Machines (SVMs) and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad-hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. Our experiments call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.

Benchmarking quantum machine learning kernel training for classification tasks

TL;DR

This study benchmarks quantum kernel methods for classification by evaluating Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) on two quantum feature maps, ZZFeatureMap and CovariantFeatureMap, across ad-hoc and standard datasets with classical baselines (SVM and Logistic Regression). QKE embeds data into a quantum feature space and computes kernel entries via state overlaps, while QKT optimizes the embedding parameters θ through a kernel-target-alignment objective, potentially using SPSA. Results show quantum methods outperform classical baselines on ad-hoc datasets but yield mixed performance on broader benchmarks, with QKT offering limited consistent gains relative to its computational cost. The findings underscore the importance of selecting an appropriate quantum feature map and tuning hyperparameters, suggesting that hyperparameter optimization may often be more impactful than QKT training in near-term quantum settings.

Abstract

Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically-crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) in connection with two quantum feature mappings, namely ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad-hoc datasets. In this study, we aim to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically Support Vector Machines (SVMs) and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad-hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. Our experiments call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
Paper Structure (18 sections, 25 equations, 4 figures, 3 tables)

This paper contains 18 sections, 25 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Kernel methods
  4. Quantum Kernel Estimation
  5. Quantum Kernel Training
  6. Classical background
  7. Quantum approximations
  8. Experimental setting
  9. Feature mappings
  10. Optimization of the kernel parameters
  11. Benchmark datasets
  12. Ad-hoc quantum datasets
  13. Reference classical datasets
  14. Classical baseline models
  15. Data pre-processing and optimization settings
  16. ...and 3 more sections

Figures (4)

  • Figure 1: P-values for t-test comparing paired classification accuracy scores in the testing set for each combination of tested models and for each dataset
  • Figure 2: Comparison of the best classical and quantum models per dataset among $n=30$ repetitions.
  • Figure 3: Differences in test accuracy score between baseline QKE and after the quantum kernel was optimized using QKT with weighted alignment. Performance values are aggregated across all datasets. P-values for paired t-tests between the corresponding metric samples are superimposed on each plot.
  • Figure 4: Relationship between evolution of the target loss and resulting accuracy score.