# Quantum speedup for twin support vector machines

## TL;DR

This paper introduces quantum algorithms that exponentially accelerate the training and prediction of twin support vector machines, enabling faster classification by leveraging quantum state preparation and distance estimation.

## Contribution

The paper presents novel quantum algorithms for TSVMs that significantly reduce computational complexity compared to classical methods.

## Key findings

- Quantum algorithms achieve $O( ext{log } mn)$ training and prediction time.
- Classical algorithms require polynomial time for training and prediction.
- Quantum methods effectively learn hyperplanes and classify data.

## Abstract

We devise new quantum algorithms that exponentially speeds up the training and prediction procedures of twin support vector machines (TSVM). To train TSVMs using quantum methods, we demonstrate how to prepare the desired input states according to classical data, and these states are used in the quantum algorithm for the system of linear equations. In the prediction process, we employ a quantum circuit to estimate the distances from a new sample to the hyperplanes and then make a decision. The proposed quantum algorithms can learn two non-parallel hyperplanes and classify a new sample by comparing the distances from the sample to the two hyperplanes in $O(\log mn)$ time, where $m$ is the sample size and $n$ is the dimension of each data point. In contrast, the corresponding classical algorithm requires polynomial time for both the training and prediction procedures.