# Chapter 13 Selected works in QML

This is a work in progress, as the vast majority of works are not present here, yet. Obviously, feel free to write at “scinawa [at] luongo . pro” for suggestions, or open an issue on github. Please understand that the aim of this section if to select relevant algorithms that can be applied for data analysis or used as other subroutines for other QML algorithms.

#### 2014

• Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning #tools, #algorithms
This paper offer two approaches for calculating distances between vectors. The idea for k-NN is to calculate distances between the test point and the training set in superposition and then use amplitude amplification tecniques to find the minimum, thus getting a quadratic speedup.

• Quantum support vector machine for big data classification Patrick #algo This was one of the first example on how to use HHL-like algorithms in order to get something useful out of them.

• Quantum Principal Component Analysis #algo The authors discovered how partial application of the swap test are sufficient to transform a quantum state $$\sigma$$ into $$U\sigma U^\dagger$$ where $$U=e^{-i\rho}$$ given the ability to create multiples copies of $$\rho$$. This work uses a particular access model of the data (sample complexity), which can be obtained from a QRAM

#### 2009

• Quantum algorithms for linear systems of equations #algo This is the paper that started everything. :) Tecniques for sparse Hamiltonian simulation and phase estimation were applied in order to estimate the singular values of a matrix. Then a controleld rotation on ancilla qubit + postselection creates a state proportional to the solution of a system of equation. You can learn more about it here.