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.

2018

Continuous-variable quantum neural networks A work presented at TQC2018 that exploit deep similarities between the mathematical formulation of NN and photinics
Classification with quantum neural networks on near term processors #variational
Artificial Quantum Neural Network: quantum neurons, logical elements and tests of convolutional nets. A new approach to qnn /. This skips complitely the unitary and gate based quantum computation Also here the model is mean to be trained by classical optimization.
Optimizing quantum optimization algorithmsvia faster quantum gradient computation #algo
Quantum Statistical Inference #phdthesis, #algo A PhD thesis on QML and other aspects of quantum information. With focus on Gaussian Processes, Quantum Bayesian Deep Learning (and other resources about causality and correlations..).
Troubling Trends in Machine Learning Scholarship #opinion-paper Is a self-autocritic of the ML community on the way they are doing science now. I think this might be relevant as well for the QML practicioner.
Quantum machine learning for data scientits #review #tutorial This is a very nice review of some of the most known qml algorithms.
Quantum algorithm implementations for beginners #review #tutorial
Quantum linear systems algorithms: a primer #review
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics #algo
The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation #algo
Applying quantum algorithms to constraint satisfaction problems #resource-estimation
Quantum Chebyshev’s Inequality and Applications #qmc

2017

Implementing a distance based classifier with a quantum interference circuit #algo
Quantum SDP solvers: Large speed-ups, optimality, and applications to quantum learning #algo
Quantum machine learning for quantum anomaly detection #algo Here the authors used previous technique to perform anomaly detection. Basically they project the data on the 1-dimensional subspace of the covariance matrix of the data. In this way anomalies are supposed to lie furhter away from the rest of the dataset.
Quantum machine learning: a classical perspective: #review #quantum learning theory
Quantum Neuron: an elementary building block for machine learning on quantum computers In the paper the authors were able to implement a neuron based on a thing called RUC-circuit (repeat until success), which allowed them to capture the nonlinearity of the sigmoid used often in the classical neuron as activation function. It is not very clear to me how to use this model to solve a problem in a data analysis.
Quantum speedup of Monte Carlo methods #algo
Improved quantum backtracking algorithms using effective resistance estimates #algo

2016

Quantum Discriminant Analysis for Dimensionality Reduction and Classification #algo Here the authors wrote two different algorithm, one for dimensionality reduction and the second for classification, with the same capabilities
An efficient quantum algorithm for spectral estimation #algo
Quantum Recommendation Systems #algo It is where you can learn about QRAM and quantum singular value estimation.

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. -Quantum walk speedup of backtracking algorithms #algo
Quantum algorithms for topological and geometric analysis of data #algo

2014

Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning #algo 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 #algo This was one of the first example on how to use HHL-like algorithms in order to get something useful out of them.
Improved Quantum Algorithm for Triangle Finding via Combinatorial Arguments #algo
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

2013

Quantum algorithms for supervised and unsupervised machine learning #algo This explain how to use swap test in order to calculate distances. Then it shows how this swap-test-for-distances can be used to do NearestCentroid and k-Means with adiabatic quantum computation
Exponential improvement in precision for simulating sparse Hamiltonians #algo

2010

Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations #algo

2009

Quantum algorithms for linear systems of equations #algo

2005

Fast quantum algorithm for numerical gradient estimation #algo

1999

The quantum query complexity of approximating the median and related statistics #algo

1996

A fast quantum mechanical algorithm for estimating the median #algo