A Triple-Hybrid Quantum Support Vector Machine Using Classical, Quantum Gate-based and Quantum Annealing-based Computing

TL;DR

This work tackles data classification by integrating three computational paradigms into a triple-hybrid quantum SVM: a gate-based quantum kernel for feature mapping, a quantum annealer solving the resulting QUBO, and classical computation for orchestration and optimization. The approach aims to improve performance on complex quantum-like data while offering faster convergence relative to purely quantum or classical SVMs. Across datasets, HQSVM shows higher precision on hard quantum data and faster convergence, though results on standard classical data are dataset-dependent, highlighting the need for hardware-aware tuning. The study demonstrates the practicality and potential of hybrid quantum-classical workflows for kernel-based learning, while acknowledging current hardware integration and noise-related limitations as important areas for future work.

Abstract

Quantum machine learning is one of the fields where quantum computers are expected to bring advantages over classical methods. However, the limited size of current computers restricts the exploitation of the full potential of quantum machine learning methods. Additionally, different computing paradigms, both quantum and classical, each have their own strengths and weaknesses. Obtaining optimal results with algorithms thus requires algorithms to be tweaked to the underlying computational paradigm, and the tasks to be optimally distributed over the available computational resources. In this work, we explore the potential gains from combining different computing paradigms to solve the complex task of data classification for three different datasets. We use a gate-based quantum model to implement a quantum kernel and implement a complex feature map. Next, we formulate a quadratic unconstrained optimisation problem to be solved on quantum annealing hardware. We then evaluate the losses on classical hardware and reconfigure the model parameters accordingly. We tested this so-called triple-hybrid quantum support vector machine on various data sets, and find that it achieves higher precision than other support vector machines (both quantum and classical) on complex quantum data, whereas it achieves varying performance on simple classical data using limited training. For the complex data sets, the triple-hybrid version converges faster, requiring fewer circuit evaluations.

Figures (4)

• Figure 1: The quantum hybrid process begins by breaking down the data into essential components needed to create a quantum circuit for the kernel. After generating the circuit, a QUBO function is prepared by sampling the quantum kernel. This QUBO is then solved and the outcomes are used to compute the $\alpha$ and $\beta$ values used in the classification function. The loss function is evaluated and fed into an optimiser, which selects the training parameters for the quantum kernel. This cycle repeats until the desired accuracy is achieved or the maximum number of iterations is reached. The orange box depicts the processes executed by a gate-based quantum computer, the green box denotes the processes executed by a quantum annealer and the blue box shows the processes carried out by a classical computer.
• Figure 2: Illustration of the average experiment results for the Qiskit dataset across various seeds, showing training points against iteration counts for each computing method, with accuracy displayed atop each bar, as detailed in Table \ref{['table:results']}.
• Figure 3: Classification maps for the qiskit dataset for different training points (seed 600) depicting blue for the -1 label and red for the +1 label are shown for both the QSVM and the hybrid QSVM methods. The circular dots in red and blue represent the training data for labels $+1$ and $-1$, respectively. The triangles in red and blue represent the testing data for labels $+1$ and $-1$, respectively.
• Figure 4: The accuracy of each method on the qiskit dataset plotted against the varying training data set sizes when predicted using the classification map trained with a size 50 training set for different seeds. The solid lines in blue are the accuracies of the QSVM method while the dotted orange lines are the accuracies of the HQSVM method.