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As we make inroads into Machine Learning, there seem to be plenty of respectable courses available online via Coursera, edX, etc. on the topic. As quantum computing is still in its infancy, not to mention, incredibly daunting, it is vital that easy to understand, introductory courses are made available.

I was able to find these courses:

Quantum Information Science I, Part 1

Quantum Optics 1 : Single Photons

However, I am not certain how relevant the second course might be.

Obviously, this question may benefit from receiving answers in the near future as the topic steadily becomes mainstream.

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    $\begingroup$ The only course that I took was Vazirani's when it was on Coursera a few years ago. It was an excellent theoretical survey for physcists. I wouldn't recommend it to general audience today. I'm afraid today the best way to learn is semi-structured: Kitaev's text + IBM Q Experience. $\endgroup$ – Aksakal almost surely binary Jul 9 '18 at 16:26
  • $\begingroup$ It matters what your prerequisites are, and what topics you want to learn, and to which level. Maybe you can make your question more precise. $\endgroup$ – Norbert Schuch Jul 10 '18 at 1:09
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I personally took the course Quantum Mechanics and Quantum Computation on EdX (UC Berkeley) by Professor Vazirani. The course is now archived, however, you can still access the lectures on YouTube. It covers the basics of quantum mechanics and gives a nice overview of some of the most popular quantum algorithms.

About this course (from the course page):

Quantum computation is a remarkable subject building on the great computational discovery that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course starts with a simple introduction to the fundamental principles of quantum mechanics using the concepts of qubits (or quantum bits) and quantum gates. This treatment emphasizes the paradoxical nature of the subject, including entanglement, non-local correlations, the no-cloning theorem and quantum teleportation. The course covers the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, Shor's quantum algorithm for factoring integers, as well as the prospects for quantum algorithms for NP-complete problems. It also discusses the basic ideas behind the experimental realization of quantum computers, including the prospects for adiabatic quantum optimization and the D-Wave controversy.

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    $\begingroup$ Oh no - it says it's not currently available. Hopefully it will become available again. $\endgroup$ – Ebony Maw Jul 8 '18 at 16:15
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    $\begingroup$ @EbonyMaw The lectures are all available on YouTube. See the link. I have the course notes in PDF if you want them. $\endgroup$ – Sanchayan Dutta Jul 8 '18 at 16:16
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    $\begingroup$ @EbonyMaw This is the first PDF lecture note. You can access the other lecture notes by changing the chapter number in the URL. $\endgroup$ – Sanchayan Dutta Jul 8 '18 at 16:32
  • $\begingroup$ Little bit ironic that the best quality work in quantum often comes from outside of physics... $\endgroup$ – Steven Sagona Jul 8 '18 at 22:49
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If you are looking for reading material instead of videos, I read John Preskill's Lecture Notes in undergrad to learn more about the subject, and thought they were really informative and well developed. They were initially written in 1997, but have modern updates from 2015.

From the website:

Course Description

The theory of quantum information and quantum computation. Overview of classical information theory, compression of quantum information, transmission of quantum information through noisy channels, quantum entanglement, quantum cryptography. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, quantum error-correcting codes, fault-tolerant quantum computation, physical implementations of quantum computation.

Prerequisites

The course material should be of interest to physicists, mathematicians, computer scientists, and engineers, so we hope to make the course accessible to people with a variety of backgrounds.

Certainly it would be useful to have had a previous course on quantum mechanics, though this may not be essential. It would also be useful to know something about (classical) information theory, (classical) coding theory, and (classical) complexity theory, since a central goal of the course will be generalize these topics to apply to quantum information. But we will review this material when we get to it, so you don't need to worry if you haven't seen it before. In the discussion of quantum coding, we will use some rudimentary group theory.

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Relatedly, there is also an EdX course on quantum cryptography. The main instructors are Stephanie Wehner and Thomas Vidick, with guest lectures by Ronald Hanson, Nicolas Gisin and David Elkouss. Its description is the following:

How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.

This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology. By the end of the course you will:

  • Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.

  • Understand quantum key distribution protocols.

  • Understand how untrusted quantum devices can be tested.

  • Be familiar with modern quantum cryptography – beyond quantum key distribution.

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I just found this: https://brilliant.org/courses/quantum-computing/, I just did the intro but the remaining is very promising.

In the end of the description:

Our focus is learning how to exploit the laws of quantum mechanics in order to compute. By the end, you'll know your way around the world of quantum information, have experimented with the ins and outs of quantum circuits, and have written your first 100 lines of quantum code — while remaining blissfully ignorant about detailed quantum physics.

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I enrolled to Introduction to Quantum Computing on Coursera.

The course provides basics of quantum computing mathematical model and then introduce basics algorithms: Deutch-Jozsa algorithm, Simon algorithm, quantum Fourier transform, Shor algorithm and Grover algorith.

The course requires understanding of linear algebra, necessary basics of quantum mechanics are explained during the course.

Interestingly, the course shows how to build single-purpose quantum computer for implementation of Deutsch-Jozsa algorithm.

The course if for free unless you want a certificate. In that case it costs $49.

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Currently there are not much courses available. However you can start with following courses:

  • Quantum Information Science II (From edX): To build up the concepts you can go through this series of courses.
  • Introduction to Quantum Computing (From Coursera): This course touches differences of quantum computers and conventional computers very well. Then going through a little quantum physics, it will land you on some specific quantum algorithms. To be very fair it is a good resource for the topics it cover but in no means suffices the needs of someone truely in quantum computing.
  • Quantum 101: Quantum Computing and Quantum Internet (From edX): This Professional Certificate will touch on all of these layers: from the devices which bridge the gap between the quantum chip and the classical control hardware, to the mathematical aspects of some quantum algorithms. The program is divided into two parts: this MOOC, the first part, will talk about the materials, four different qubits and operations on these qubits. The second MOOC, "Architecture, Algorithms, and Protocols of a Quantum Computer and Quantum Internet". By completing both parts, you will have a complete overview of all building blocks of a quantum computer.
  • The Quantum Internet and Quantum Computers: How Will They Change the World? (From edX): After completing the above professional certificate you can continue on to this course. This course will provide you with a basic understanding of quantum computing and the quantum internet. You’ll explore various application areas, such as quantum chemistry, quantum machine learning, encryption and secure communication, factorization, and blind quantum computation.

Then, to focus a particular area, you can go for:

  • Quantum Machine Learning (From edX): It will cover topics like : Distinguish between quantum computing paradigms relevant for machine learning, Assess expectations for quantum devices on various time scales, Identify opportunities in machine learning for using quantum resources, Implement learning algorithms on quantum computers in Python
  • Quantum Cryptography (From edX): This will cover: Fundamental ideas of quantum cryptography, Cryptographic concepts and tools: security definitions, the min-entropy, privacy amplification, Protocols and proofs of security for quantum key distribution, The basics of device-independent quantum cryptography Modern quantum cryptographic tasks and protocols
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Maybe be a bit of left field but I found Peter Wittek - may he Rest In Peace - course on edX quite good.

https://www.edx.org/course/quantum-machine-learning

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