Adiabatic Quantum Support Vector Machines

TL;DR

This work tackles the computational burden of training support vector machines by recasting SVM training as a QUBO suitable for adiabatic quantum computing on the D-Wave Advantage. The authors provide a theoretical analysis showing an $\mathcal{O}(N^2)$-time/space scaling relative to the classical $\mathcal{O}(N^3)$ baseline (with fixed precision), and they demonstrate practical speedups up to about $4.5\times$ on large-feature datasets while achieving accuracies that are on par with a Scikit-learn SVM on several benchmarks. The results indicate potential quantum advantages for ML training on near-term hardware, albeit with overheads from embedding and hardware constraints, and they identify directions for kernel extensions and noise-mitigation in future work.

Abstract

Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic quantum approach for training support vector machines. We show that the time complexity of our quantum approach is an order of magnitude better than the classical approach. Next, we compare the test accuracy of our quantum approach against a classical approach that uses the Scikit-learn library in Python across five benchmark datasets (Iris, Wisconsin Breast Cancer (WBC), Wine, Digits, and Lambeq). We show that our quantum approach obtains accuracies on par with the classical approach. Finally, we perform a scalability study in which we compute the total training times of the quantum approach and the classical approach with increasing number of features and number of data points in the training dataset. Our scalability results show that the quantum approach obtains a 3.5--4.5 times speedup over the classical approach on datasets with many (millions of) features.

Figures (6)

• Figure 1: SVMs.
• Figure 2: Comparison of hyperplanes created by the support vectors with Scikit-learn (+), simulated annealing(- -), and D-Wave (---) on positive synthetic data (blue and green circles).
• Figure 3: Comparison of hyperplanes created by the support vectors with Scikit-learn (+), simulated annealing(- -) and D-Wave (---) on negative synthetic data (blue and green circles).
• Figure 4: Comparison of hyperplanes created by the support vectors with Scikit-learn (+), simulated annealing(- -), and D-Wave (---) on random synthetic data (blue and green circles split by classification).
• Figure 5: Scalability comparison of the Scikit-learn SVM (blue bar and bold line) and quantum SVM (light, medium, and dark green bars and dotted line). The $x$-axis indicates the number of features ($d$), and the $y$-axis logarithmically represents time in seconds. The $x$-axis ranges from $2$ to $8,388,608$ across the two figures. In Figure \ref{['fig:svm-scaling-d-small']}, $d$ varies between $2$ and $4,096$, and in Figure \ref{['fig:svm-scaling-d-large']}, $d$ varies between $8,192$ and $8,388,608$. In Figure \ref{['fig:svm-scaling-d-large']}, at 8 million features, the quantum approach demonstrated a speedup of 3.69$\times$ over the classical approach.