Quantum Support Vector Machine without Iteration

TL;DR

This paper introduces a quantum support vector machine that eliminates repetitive processes using amplitude estimation, reducing resource requirements and improving efficiency in quantum machine learning tasks.

Contribution

The paper proposes AE-QSVM, a novel quantum SVM that avoids iteration by employing quantum amplitude estimation, enhancing resource efficiency and accuracy.

Findings

AE-QSVM reduces quantum resource consumption.

The algorithm achieves high classification accuracy.

Experimental results show advantages over previous methods.

Abstract

Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the classification. However, as the output states of a previous test cannot be reused for a new test in the Swap Test, the quantum algorithm LS-QSVM has to be repeated in preparing qubits, manipulating operations, and carrying out the measurement. This paper proposes a QSVM based on the generalized quantum amplitude estimation (AE-QSVM) which gets rid of the constraint of repetitive processes and saves the quantum resources. At first, AE-QSVM is trained by using the quantum singular value decomposition. Then, a query sample is classified by using the generalized quantum amplitude estimation in which high accuracy can be achieved by adding auxiliary qubits instead of repeating the algorithm. The complexity of AE-QSVM is reduced to $O(\kappa^{3}\varepsilon^{-3}(log(mn)+1))$ with an accuracy $\varepsilon$, where $m$ is the number of training vectors, $n$ is the dimension of the feature space, and $\kappa$ is the condition number. Experiments demonstrate that AE-QSVM is advantageous in terms of training matrix, the number of iterations, space complexity, and time complexity.