Quantum support vector machine without iteration

Abstract

Quantum algorithms can enhance machine learning in different aspects. The quantum support vector machine was proposed to improve the performance, in which the Swap Test plays a crucial role in realizing the classification. However, as the Swap Test is destructive, the quantum support vector machine must be repeated in preparing qubits and manipulating operations. This paper proposes a quantum support vector machine based on the amplitude estimation (AE-QSVM) which gets rid of the constraint of repetitive process and saves the quantum resources. At first, a generalized quantum amplitude estimation is introduced in which the initial state can be arbitrary instead of being |0〉. Then, AE-QSVM is trained by the quantum singular value decomposition and a query sample is classified by the generalized quantum amplitude estimation. In AE-QSVM, a high accuracy can be achieved by adding auxiliary qubits instead of repeating the algorithm. The time and space complexity of AE-QSVM are reduced compared with other algorithms. Finally, we ran experiments on the IBM's quantum computer and experimental results demonstrate that classification with a 95% probability of success only uses 12 qubits.