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arXiv:2210.02355 · Quantum Machine Intelligence

A kernel-based quantum random forest for improved classification

Maiyuren Srikumar, Charles D. Hill, Lloyd C. L. Hollenberg

Published Feb 7, 2024• 28 citations
arXivHTMLPDF
DOI
10.1007/s42484-023-00131-2

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A typical problem that is solved by supervised machine learning techniques is classification. There are many types of this problem, such as binary classification, multi-classification, and multi-labels. The development of techniques that perform well in different types of classification problems, and for datasets with many or few variables, or many or few data, remains a challenge. On the other hand, recent work indicates that machine learning can benefit from quantum computing in terms of reducing computational complexity and improving its performance. The purpose of this research is to analyze the use of Quantum Support Vector Machines (QSVM) for different types of classification problems. For this, several kernels (linear and Gaussian) are considered. In turn, a comparison is made with Random Forest. Also, a detailed analysis is carried out for the binary classification of coffee beans, obtaining a precision of 95% and an accuracy of 79%.
This paper introduces a Bayesian Optimization-based Multiple Kernel Quantum Support Vector Machine (BO-MKQSVM) to overcome the limitations of traditional Quantum Support Vector Machines (QSVMs), where a single kernel's representational power is insufficient, and multi-kernel weight optimization is complex. By integrating multiple quantum feature maps and leveraging Bayesian Optimization, the method automatically tunes kernel weights and regularization parameters, thereby enhancing model performance and generalization ability in small-sample classification. Experiments on publicly available datasets, including Iris, Fertility, and Immunotherapy, show that BO-MKQSVM outperforms classical models such as SVM, Random Forest, Gradient Boosting Decision Trees, and Multilayer Perceptrons in accuracy, recall, and F1-score, demonstrating superior classification performance and robustness.
Credit default prediction is a tabular classification problem in which modest gains in F1 translate directly into reduced financial exposure. We ask whether Instantaneous Quantum Polynomial-time (IQP) circuits can produce features that improve a classifier over both its raw classical baseline and Kernel PCA - the strongest unsupervised classical non-linear alternative - at an equal feature budget. The dataset provides 23 financial attributes per client; for an n-qubit circuit we select n of them, encode each as a rotation angle, and read 2n expectation values back out as new features. The motivation for using a quantum circuit is computational: an n-qubit IQP circuit runs in constant depth and encodes feature correlations in a 2^n-dimensional Hilbert space, whereas classical simulation of its exact output statistics scales exponentially in n. Using the UCI Default of Credit Card Clients dataset and five-fold cross-validation, we find that appending 16 IQP features (n = 8 qubits) to a Logistic Regression model raises F1 from 0.462 to 0.517 (+0.055, p < 0.0001). Kernel PCA, the next-best method, reaches only 0.493 at the same feature count; the gap survives Benjamini-Hochberg correction across 12 tests (p = 0.00007). No other classifier - Random Forest, SVM, XGBoost, or k-NN - benefits, which points to a linear-expressivity mechanism rather than a generic improvement. We also show that how the 8 input features are chosen matters: Random Forest importance-guided selection reaches F1 = 0.523, while encoding maximally uncorrelated features drops it to 0.496, demonstrating that the circuit amplifies informative structure rather than creating it from scratch.