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Variational Algorithms and Conclusions obtained from the thesis

Agustin Bignu
Jul 17 · 5 min read

This is the last article of the series of articles on my final thesis on Quantum Machine Learning. We have covered a wide range of topics with quantum computing and machine learning. You can check the previous articles entering my profile, they are in order.

In this last article, we will see what variational algorithms are and we are going to give some final thoughts and conclusions obtained throughout the work.

Variational Algorithms

Quantum computing is a discipline that, within today's technology, is difficult to study. Mainly, this is due to the fact that we lack the technology to develop perfect quantum computers. In other words, our current quantum computers are not perfect. In this sense, we can’t execute quantum algorithms in the way we wish. For that reason, since 2012 researchers have been developed hybrid quantum-classical algorithms called variational algorithms.

This kind of algorithms seeks to attack complex problems using near term quantum computers as well as classical computers. Many algorithms have been developed and are being currently developed.

Nowadays there are many variational algorithms:

  • Variational Quantum Eigensolver (VQE)
  • Quantum Adiabatic Optimization Algorithm (QAOA)
  • Quantum Neural Networks (QNN)
  • Quantum Support Vector Machines (QSVM)
  • Variational Quantum Classifier (VQC)
  • Quantum GAN (QGAN)

this to name a few. All of them are available in libraries such as Qiskit (IBM) [1], Strawberry Fields (Xanadu) [2] or Penny Lane (Xanadu) [3].

These libraries use quantum optimization techniques to perform machine learning or, in the other way, machine learning techniques to learn a quantum state or pattern.

In future articles, we will explore some applications of these algorithms using the libraries mentioned above.

Final conclusions from the thesis

In this last section, we will explain the conclusions obtained throughout the work. In turn, future views and a brief personal opinion on the subject will be discussed.

The main objective of the work was to see if AI and quantum computing could work together. The answer to this objective is affirmative. What is more, it is one of the research branches within Physics, Computer Science and Mathematics with the brightest future. Quantum machine learning has a direct connection with Physics since it is based on quantum computing, making it ideal to simulate quantum systems.

Nowadays, research in this field is led by the private sector, with companies such as Google, IBM, and D-Wave Systems being the most prominent. We also find future collaborations such as the one Volkswagen and Google have in order to implement quantum computing in traffic optimization [4].

Taking into consideration everything said throughout the work we can conclude that there are, for now, two main branches of work in quantum machine learning. The first one is to use the probabilistic description of quantum theory to describe stochastic processes. This approach is used for probabilistic sampling in the case of Boltzmann machines (see article), for Bayes’ law in the case of having to distinguish between quantum states (see article) and in Markov processes for quantum reinforcement learning (see article). Second, many researchers try to find quantum algorithms that supplant classical machine learning algorithms to solve a particular problem. They show that it can be improved in terms of the complexity of the problem to be solved. This is true for algorithms such as the quantum SVM versus the classical one (see article) where the computational power of quantum computers helps us attack the complex optimization calculations.

Currently, the approach does not vary from the two mentioned above. Researchers try to take advantage of quantum computers since they have greater power for calculation than classical computers. This is because of superposition and the probabilistic nature of quantum theory that makes easier to face probabilistic sampling or, as mentioned, describe and model stochastic processes.

Despite the advantages mentioned so far, we can find disadvantages that hinder the process of this discipline.

While quantum algorithms provide enormous advantages in data processing they hardly do so at the time of reading them. This means that what it costs to read the data can come to dominate, in some cases, the cost of quantum algorithms. Thinking about the Big Data era, this is something that must be solved in the short term if we want to use quantum machine learning for tasks in this area.

In the area of supervised learning, the model learns from the output data. Taking this to the case of quantum computing, learning the complete solution of some quantum algorithms as a bit string requires learning an exponential number of bits, which makes some applications of quantum machine learning unfeasible. This problem could be overcome in the short term by making statistics about the output data and learning from them. However, it is something that must be worked on.

On the other hand, the hardware that this discipline requires is something quite innovative and that is constantly changing and under research. Nowadays, this topic is one of the main obstacles with which quantum machine learning research is facing.

Looking ahead, it is not expected its growth to be stopped. Furthermore, new research branches will be developed in order to make applications to the industry. A possible way to move forward would be to study applications to quantum rather than classical data. This would allow us to understand better the quantum computers. It would also generate a virtuous circle as the one happened in the classic computing making their advance much faster in terms of technology. At the same time, the development of efficient hardware is also a path that must be worked on and that will require a lot of research

Lastly, I will mention my personal thoughts on the subject. In order to understand the importance that this discipline will have in the future, an analogy can be made. Quantum machine learning and quantum computing can be compared to how computer science and classical computing were in the 40s and 50s. From that moment on, it was when it boomed and much of the technology and theoretical basis on which the computers that are used today are sustained were achieved. So there is still much work to be done.


To sum up, I would like to thank everyone that followed this series of articles. If you have any kind of request or question you can mail me to

I will keep posting about QML: tutorials, explanation of different techniques and algorithms. Stay tuned!

You can find me on LinkedIn:

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Keep it up!





[4]Volkswagen, Google Kooperation. November 2017.

Data Driven Investor

from confusion to clarity, not insanity

Agustin Bignu

Written by

Physicist. Machine Learning and Data Science enthusiast.

Data Driven Investor

from confusion to clarity, not insanity

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