Variational Quantum Linear Solver Enhanced Quantum Support Vector Machine

Nouhaila Innan, Muhammad Al-Zafar Khan, B. Panda +1 more

Jianming Yi, Kalyani Suresh, Ali Moghiseh +1 more

Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate Scale Quantum (NISQ) devices. In this work, we propose a novel approach called the Variational Quantum Linear Solver (VQLS) enhanced QSVM. This is built upon our idea of utilizing the variational quantum linear solver to solve system of linear equations of a Least Squares-SVM on a NISQ device. The implementation of our approach is evaluated by an extensive series of numerical experiments with the Iris dataset, which consists of three distinct iris plant species. Based on this, we explore the effectiveness of our algorithm by constructing a classifier capable of classification in a feature space ranging from one to seven dimensions. Furthermore, we exploit both classical and quantum computing for various subroutines of our algorithm, and effectively mitigate challenges associated with the implementation. These include significant improvement in the trainability of the variational ansatz and notable reductions in run-time for cost calculations. Based on the numerical experiments, our approach exhibits the capability of identifying a separating hyperplane in an 8-dimensional feature space. Moreover, it consistently demonstrated strong performance across various instances with the same dataset.

Hong Li, Nan Jiang, Rui Zhang +2 more

Jianming Yi, Kalyani Suresh, Ali Moghiseh +1 more

Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate Scale Quantum (NISQ) devices. In this work, we propose a novel approach called the Variational Quantum Linear Solver (VQLS) enhanced QSVM. This is built upon our idea of utilizing the variational quantum linear solver to solve system of linear equations of a least squares-SVM on a NISQ device. The implementation of our approach is evaluated by an extensive series of numerical experiments with the Iris dataset, which consists of three distinct iris plant species. Based on this, we explore the practicality and effectiveness of our algorithm by constructing a classifier capable of classification in a feature space ranging from one to seven dimensions. Furthermore, by strategically exploiting both classical and quantum computing for various subroutines of our algorithm, we effectively mitigate practical challenges associated with the implementation. These include significant improvement in the trainability of the variational ansatz and notable reductions in run-time for cost calculations. Based on the numerical experiments, our approach exhibits the capability of identifying a separating hyperplane in an 8-dimensional feature space. Moreover, it consistently demonstrated strong performance across various instances with the same dataset.

Jie Lin, Dan-Bo Zhang, Shuo Zhang +3 more

Siheon Park, Daniel K. Park, June‐Koo Kevin Rhee

Abstract A kernel-based quantum classifier is the most interesting and powerful quantum machine learning technique for hyperlinear classification of complex data, which can be easily realized in shallow-depth quantum circuits such as a SWAP test classifier. A variational quantum approximate support vector machine (VQASVM) can be realized inherently and explicitly on these circuits by introduction of a variational scheme to map the quadratic optimization problem of the support vector machine theory to a quantum-classical variational optimization problem. Probability weight modulation in index qubits of a classifier can designate support vectors among training vectors, which can be achieved with a parameterized quantum circuit (PQC). The classical parameters of PQC is then transferred to many copies of other decision inference circuits. Our VQASVM algorithm is experimented with toy example data sets on cloud-based quantum machines for feasibility evaluation, and numerically investigated to evaluate its performance on a standard iris flower and MNIST data set. The empirical run-time complexity of VQASVM is estimated to be sub-quadratic on the training data set size, while that of the classical solver is quadratic.