In the past few days, I have been trying to collect material (mostly research papers) related to Quantum machine learning and its applications, for a summer project. Here are a few which I found interesting (from a superficial reading):

However, coming from the more physics-y end of the spectrum, I don't have much background knowledge in this area and am finding most of the specialized materials impenetrable. Ciliberto et al.'s paper: Quantum machine learning: a classical perspective somewhat helped me to grasp some of the basic concepts. I'm looking for similar but more elaborate introductory material. It would be very helpful if you could recommend textbooks, video lectures, etc. which provide a good introduction to the field of quantum machine learning.

For instance, Nielsen and Chuang's textbook is a great introduction to the quantum computing and quantum algorithms in general and goes quite far in terms of introductory material (although it begins at a very basic level and covers all the necessary portions of quantum mechanics and linear algebra and even the basics of computational complexity!). Is there anything similar for quantum machine learning?

P.S: I do realize that quantum machine learning is a vast area. In case there is any confusion, I would like to point out that I'm mainly looking for textbooks/introductory papers/lectures which cover the details of the quantum analogues of classical machine learning algorithms.


5 Answers 5


The Nielsen and Chuang of Quantum Machine Learning is this extensive review called "Quantum Machine Learning" published in Nature in 2017. The arXiv version is here and has been updated as recently as 10 May 2018.

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    $\begingroup$ This looks good. Here's another review paper from 2014, which I found useful: arXiv:1409:3097. $\endgroup$ Commented May 27, 2018 at 7:16
  • $\begingroup$ Yes, a bit older but also great. I know all three authors and do endorse their work. Keep in mind "quantum machine learning" is still a new topic, and many of the authors of the Nature paper have said that most of the time spent on that paper was on arguing over what the field even is. Therefore it's a bit early for there to be a perfect introduction like Nielsen and Chuang is for quantum computing, but the Nature paper, combined with the paper you suggested, is probably the best. $\endgroup$ Commented May 27, 2018 at 7:30
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    $\begingroup$ this is definitely not a "Nielsen and Chuang" of QML. It is a review paper and as such not much more than a list of references, with a few words attached, to what has been and is being done in the field (not that this is bad in any way: the paper perfectly achieves its purpose). I would say that Wittek's book on quantum machine learning is a better fit for such a title, but really the field is not mature enough yet to have anything equivalent to a "N&C of QML" $\endgroup$
    – glS
    Commented May 29, 2018 at 17:28
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    $\begingroup$ This review has just about 14 pages in single column. This is hardly an "extensive review" (e.g., Rev. Mod. Phys. papers have about 40 pages in 2-column). Not to mention that it cannot be compared to a book like Nielsen and Chuang with its about 600 pages. $\endgroup$ Commented Nov 24, 2018 at 21:52
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    $\begingroup$ This review paper over-emphasizes use of oracle-based algorithms like HHL, which is understandable given the author list but hardly representative of the field. $\endgroup$
    – forky40
    Commented May 30, 2019 at 19:07

Here's a list of other resources to learn about quantum machine learning:

An introduction to quantum machine learning

The quest for a Quantum Neural Network

Quantum Machine Learning: What Quantum Computing Means to Data Mining

Quantum Machine Learning 1.0


The most recent quantum machine learning textbook is

Schuld and Petruccione (2018). Supervised Learning with Quantum Computers

while a nice companion to Nielsen and Chuang for introductory quantum maths is

Marinescu and Marinescu (2011). Classical and Quantum Information, Chapter 1: Preliminaries


A lot of focus in quantum machine learning in the near term revolves around variational quantum algorithms (you'll also see them called variational quantum circuits or parameterized quantum circuits), as well as their extensions to hybrid classical-quantum models. Though the field is evolving pretty fast, this recent review article gives a fairly good overview:

Benedetti et al (2019). Parameterized quantum circuits as machine learning models

I would certainly recommend it over the Nature paper mentioned above if you are intereted in the emerging near-term viewpoint.

We've also been curating a number of explanatory QML materials and code demos over at pennylane.ai/qml which might be helpful for people trying to learn the field.


Here is an introductory course taught by Dr. Peter Wittek. Although it is archived, you can still view the lectures for free.

Dr. Wittek also published this book on QML.


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