---
# System prepended metadata

title: '[[WIP]A rigorous and robust quantum speed-up in supervised machine learning](https://arxiv.org/abs/2010.02174)'
tags: [' quantum machine learning', ' quantum computing', quantum kernel estimation, ' 2020']

---

---
tags: quantum kernel estimation, quantum machine learning, quantum computing, 2020
---

# [[WIP]A rigorous and robust quantum speed-up in supervised machine learning](https://arxiv.org/abs/2010.02174)
Yunchao Liu, Srinivasan Arunachalam, Kristan Temme

## Abstract
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear if quantum speed-ups still exist without making these strong assumptions, or are heuristic in nature with no provable advantage over classical algorithms. In this paper, we establish a rigorous quantum speed-up for supervised classification using a general-purpose quantum learning algorithm that only requires classical access to data. Our quantum classifier is a conventional support vector machine that uses a fault-tolerant quantum computer to estimate a kernel function. Data samples are mapped to a quantum feature space and the kernel entries can be estimated as the transition amplitude of a quantum circuit. We construct a family of datasets and show that no classical learner can classify the data inverse-polynomially better than random guessing, assuming the widely-believed hardness of the discrete logarithm problem. Meanwhile, the quantum classifier achieves high accuracy and is robust against additive errors in the kernel entries that arise from finite sampling statistics.

## Backgrounds


## Methods


## Open Problems