Variational quantum kernel classifier based on support vector machine for big data classification

Abstract

A kernel-based quantum classifier is the most interesting and powerful quantum machine learning technique for the hyper-linear 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 the 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 are then transferred to many copies of other decision inference circuits. Our VQASVM algorithm has experimented with ad hoc example datasets on cloud-based quantum machines for feasibility evaluation. It is numerically investigated on a standard iris flower and MNIST dataset to evaluate its scalability and trainability. The empirical run-time complexity of VQASVM is estimated to be sub-quadratic on the training dataset size, while that of the classical solver is quadratic.