July 19, 2018

# Selected articles on Quantum Machine Learning

This is a collection of paper I have found useful in the last years. It is far from complete and you are welcome to suggest new entries here that you think I have missed. I don’t claim for completeness though.

#### 2015

• Advances in quantum machine learning #implementations, #review
It cover things up to 2015, so here you can find descriptions of Neural Networks, Bayesian Networks, HHL, PCA, Quantum Nearest Centroid, Quantum k-Nearest Neighbour, and others.

##### 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 self-testing #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.