Real-Part Quantum Support Vector Machines

In recent years, quantum computing has been slowly transitioning from a purely theoretical branch of computer science to a practical yet highly experimental discipline. Within quantum computing, quantum machine learning is becoming more and more popular. However, subtle differences between classical and quantum machine learning methods sometimes lead to incompatible formalizations of otherwise well aligned methods. Inspired by this observation, we investigate a classical machine learning method, namely support vector machines, and compare the model to state-of-the-art quantum support vector machines (QSVM). We show that the training procedure for QSVMs does not perform margin maximization, thus deviating from the strict definition of SVMs. Moreover, we propose a novel Real-Part QSVM formulation that overcomes this issue. We prove that our Real-Part QSVM converges to the classical SVM, while enjoying a logarithmic space complexity. Results obtained from quantum simulations as well as from a 27-qubit superconducting quantum processor confirm our theoretical findings. The source code is available at: https://github.com/np84/realqsvm.