Real-Part Quantum Support Vector Machines

With the rise of new quantum computing architectures, quantum computing is slowly leaving the realm of a purely theoretical branch of computer science—becoming 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. We exemplify this dilemma by taking the example of quantum support vector machines (QSVM). We prove that the QSVM training procedure does not perform margin maximization, and hence, is not an SVM in a strict sense.
Moreover, we propose a novel QSVM formulation that overcomes this issue.
We prove that our novel Real-Part QSVM converges to the classical SVM in the limit of infinite quantum measurements, while enjoying a logarithmic space complexity. Results obtained from quantum simulations as well as an 27-qubit superconducting quantum processor confirm our theoretical findings.