Autor : Phd. Hamza Jaffali, Researcher at ColibrITD

# Introduction

The goal of Machine Learning is to teach the machine how to perform a specific task, without providing explicit instructions. It is divided in three main families: **supervised **learning (*teaching by example*), **unsupervised **learning (*clustering*and *dimensional reduction*) and **reinforcement **learning (*trial/error, behaviorism*).

When one talks about Quantum Machine Learning (QML), it can refer to three different approaches. The first one is to apply Classical Machine Learning (CML) to solve problems in quantum physics or quantum information. The second one is to use quantum computations to speedup classical machine learning techniques, sometimes leading to hybrid algorithms. This is also known as Quantum-Enhanced Machine Learning. The last one is to use pure quantum models or adaptions of learning algorithms to exploit the whole potential of Quantum Mechanics and Quantum Information Processing.

## Why Quantum Machine Learning ?

Nowadays, our society is facing different kinds of challenges. Providing a solution to these difficulties can help our world better organize itself and leave to next generations a stable heritage. In the recent years, with the development of Machine Learning techniques, many problems have been tackled using these algorithms with the help of a large amount of collected data.

However, when considering the most difficult problems challenging our society, actual machine learning algorithms and approaches show some limitations in terms of the size and amount of data that can be processed, but also from the point of view of efficiency and performance.

Quantum Machine Learning has the potential, by exploiting the advantages of Quantum Computing and Quantum Information Processing, to help machines learn faster and tackle more difficult tasks.

“Simulating the behavior of 100 billion neurons of human brain is not feasible by classical computer but quantum machine learning promises to fulfill that requirement”

Amit Ray

## Actual state of the art

In this article, our goal is not to focus on the first approach of QML, since we want focus on algorithms and techniques involving quantum computations, even if we can find interesting applications of Classical Machine Learning to Quantum Mechanics [4, 36, 21, 44, 32].

We rather talk about the produced work concerning quantum-enhanced machine learning, and pure quantum machine learning algorithms. We will divide this overview following the well known three families.

## Supervised Learning

Supervised Learning is certainly the most famous and developed aspect of Machine Learning, both in academic and industrial research. It is also the case in Quantum Machine Learning, since many works tried to adapt classical supervised algorithms to the quantum setup [47, 38].

Neural networks are one of the most used supervised algorithms, because of their ability to classify and make accurate predictions. Several models of quantum neural networks and quantum perceptron were proposed in the literature, with different ways of encoding data [34, 53, 39, 55, 17, 52, 35]. Several improvements in the training were proposed using quantum optimization or other methods [31, 5], leading to few first applications [7, 17].

Another well-known algorithm is the Support Vector Machines, which purpose is to find the optimal hyperplane to spatially separate the data into classes, according to the training dataset. In the quantum version, the kernel (or feature map) can for instance be replaced by an efficient quantum computation of the overlap between two states encoding the datapoints. Several works [50, 11, 8, 46, 19, 29] were produced about Quantum Support Vector Machines since the first article was published on this subject in 2014 [43].

One can also mention an adaption of Ensemble Learning (sometimes called Boosting) to Quantum Computing with QBoost [37].

In most of the present works, an exponential speed-up is claimed but it is not always rigorously verified when considering practical implementations of such algorithms. In a recent paper [13], the limits of Quantum Supervised Learning are discussed, claiming that at most it can show polynomial speedups over its classical counterpart.

## Unsupervised Learning

Quantum Computing was also introduced in several Unsupervised Learning algorithms, providing new quantum-enhanced machine learning algorithms.

Quantum Principal Component Analysis (qPCA), first proposed by Llyod *et al. *[31] in 2014, exploits the spectral decomposition of the Variational Quantum Eigensolver. Many works were derived from it, providing improvements in the performance or precision of qPCA [27, 48, 20, 18]. Recently qPCA was used in finance to simulate Heath-Jarrow-Morton model for pricing interest-rate financial derivatives [33].

The K-means and nearest-neighbors algorithms were also adapted, leading to the Q-means algorithm for instance. These clustering algorithms exploit the efficiency of quantum computer for computing distances, and several versions were proposed in the literature [1, 30, 54, 22, 6, 26]. A recent experimental implementation of this algorithm was proposed on photonic quantum computers [9]. We can also cite another work with the same unsupervised approach [10] for state tomography.

## Reinforcement Learning

Reinforcement Learning has received less interest than the two other approaches of machine learning, but interesting propositions were made anyway.

Most of the works are based on the agent model [40, 16], where an agent interacts with his environment and select the best actions to maximize a reward function, as it was first proposed in [15].

Different approaches were also used to implement Quantum Reinforcement Learning, such as Boltzmann machines [14] and Variational Quantum Circuits [12]. This algorithm was applied recently for maximizing the overlap between two states [3] or for estimating eigenvectors of a given observable [2].

Experimental realizations using superconducting circuits [25], quantum optical neural networks [49] or photonic systems [23] were proposed in the literature, sometimes showing in practice an experimental speedup [45].

## Existing tools

There already exists some packages and libraries allowing one to combine classical and quantum computations to implement quantum machine learning.

We first can mention PennyLane, an open-source software from Xanadu for performing simulations of Quantum Machine learning. It combines classical machine learning packages with quantum simulators and hardware.

The famous Qiskit environment provides a package Aqua, allowing to implement Quantum SVM and the associated feature map. However, it must be combined with other classical packages.

The new tool TensorFlow Quantum, published by Google, integrates Cirq and TensorFlow, and offers high-level abstractions for implementing quantum-classical model.

On another hand, QML is a python compatible toolkit [42], but not a high-level framework. It only provides functionalities to launch simulations.

Another one is Paddle Quantum, an open-source QML toolkit based on Baidu PaddlePaddle (the first open-source and industrial level deep learning platform in China) and uses the quantum simulator of Baido from Institute for Quantum Computing.

Finally, Q#, developed by Microsoft provide a development toolkit for machine learning and quantum algorithms.

We also mention AWS with Amazon Bracket, Tequila [24], tket (Cambridge Quantum Computing), Strawberry Fields [51] and Forest (Rigetti’s software library), which can in the future provide programming blocks or libraries for Quantum Machine Learning.

Most of these projects are referenced in [28].

## At ColibrITD

At ColibrITD, we aim to work at the highest level of abstraction and place ourself at the top layer in the quantum software ecosystem.

In fact, our project is to implement a full stack quantum software framework composed of three level of actions: first, translating classical to quantum code, secondly, modeling and optimizing quantum computations on our quantum engine and, finally, executing them on the right available hardware device.

One of the first applications and usecases for our framework we selected is to deal with Quantum Reinforcement Learning algorithms. We aim to develop the first Quantum Reinforcement Learning platform for solving various problems by leveraging quantum computations and the associated speed-up.

We believe at ColibrITD that Quantum advantage should be brought for everyone, and developing an automated tool that can translate classical Reiforcement Learning algorithms to the quantum setup is one of our mission.

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