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Quantum computing for the determined

by Michael Nielsen on June 10, 2011

I’ve posted to YouTube a series of 22 short videos giving an introduction to quantum computing. Here’s the first video:

Below I list the remaining 21 videos, which cover subjects including the basic model of quantum computing, entanglement, superdense coding, and quantum teleportation.

To work through the videos you need to be comfortable with basic linear algebra, and with assimilating new mathematical terminology. If you’re not, working through the videos will be arduous at best! Apart from that background, the main prerequisite is determination, and the willingness to work more than once over material you don’t fully understand.

In particular, you don’t need a background in quantum mechanics to follow the videos.

The videos are short, from 5-15 minutes, and each video focuses on explaining one main concept from quantum mechanics or quantum computing. In taking this approach I was inspired by the excellent Khan Academy.

The course is not complete — I originally planned about 8 more videos. The extra videos would complete my summary of basic quantum mechanics (+2 videos), and cover reversible computing (+2 videos), and Grover’s quantum search algorithm (+4 videos). Unfortunately, work responsibilities that couldn’t be put aside meant I had to put the remaining videos on hold. If lots of people work through the existing videos and are keen for more, then I’ll find time to finish them off. As it is, I hope the incomplete series is still useful.

One minor gotcha: originally, I was hoping to integrate the videos with a set of exercises. Again, time prevented me from doing this: there are no exercises. But as a remnant of this plan, in at least one video (video 7, the video on unitary matrices preserving length, and possibly elsewhere) I leave something “to the exercises”. Hopefully it’s pretty clear what needs to be filled in at this point, and viewers can supply the missing details.

Let me finish with two comments on approach. First, the videos treat quantum bits — qubits — as abstract mathematical entities, in a way similar to how we can think of conventional (classical) bits as 0 or 1, not as voltages in a circuit, or magnetic domains on a hard disk. I don’t get into the details of physical implementation at all. This approach bugs some people a lot, and others not at all. If you think it’ll bug you, these videos aren’t for you.

Second, the videos focus on the nuts-and-bolts of how things work. If you want a high-level overview of quantum computing, why it’s interesting, and what quantum computers may be capable of, there are many available online, a Google search away. Here’s a nice one, from Scott Aaronson. You may also enjoy David Deutsch’s original paper about quantum computing. It’s a bit harder to read than an article in Wired or Scientific American, but it’s worth the effort, for the paper gives a lot of insight into some of the fundamental reasons for thinking about quantum computing in the first place. Such higher-level articles may be helpful to read in conjunction with the videos.

Here’s the full list of videos, including the first one above. Note that because this really does get into the nuts and bolts of how things work, it also builds cumulatively. You can’t just skip straight to the quantum teleportation video and hope to understand it, you’ll need to work through the earlier videos, unless you already understand their content.

The basics

Superdense coding

Quantum teleportation

The postulates of quantum mechanics (TBC)

Thanks to Jen Dodd, Ilya Grigorik and Hassan Masum for feedback on the videos, and for many enjoyable discussions about open education.

If you enjoyed these videos, you may be interested in my forthcoming book, Reinventing Discovery, where I describe how online tools and open science are transforming the way scientific discoveries are made.

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  1. Wow, super Michael. I feel back in the days when I was reading your book. I’ll spend some time this week end to watch part of the seri

  2. And just a few days a go I was thinking about pursuing a career in quantum computing. You have just made my day sir.

    One thing though – what sort of major(s) would I have to pursue in order to work in the field of quantum computing?

    [MN: It depends somewhat on what University you’re at, what they focus on, and what your interests are. Aside from looking around online to see what you’ll need to know, and what your interests are, you might also get some useful advice from student advisors in any departments that seem relevant (e.g., physics, computer science, mathematics).]

  3. On behalf of humanity, thanks for your time invested in this project.

    [Thanks Pete! – MN]

  4. krabsa permalink

    Thanks for taking the time to do this.

  5. Thanks! I am now watching the 2nd video about ‘working with qubits’ and you are explaining it very clearly. Especially great that you don’t skip over the notation things, that would otherwise confuse me a lot!

  6. Rishi permalink

    Amazing work – much appreciated. Any chance you could give us a download link for the set of videos?

  7. just finished the first one – fantastic. thank you SO much.

  8. Jesse permalink

    Awesome series, thank you so much for doing it. I got about 1 minute into the first video before I decided that you need to be the recipient of a Wacom tablet donation!

  9. Anthony Lozano permalink

    These are going to be great! I can’t wait to watch more.

  10. Great topic. By the way, I want your microphone! No really, great post and coverage!

  11. Stefano Pigozzi permalink

    awesome stuff I watched the first 3 videos and I’m already hooked

  12. Madhu Challa permalink

    awesome !!! now i can keep myself occupied 🙂 thanks

  13. Thanks for doing this. Repeating the request above – would you consider making a ‘complete set’ download link or torrent to save having to use the youtube site?

  14. Eric Christiansen permalink

    Thank you! Have you considered publishing an archive of all these videos via bittorrent? I prefer to consume lectures at 2x speed or greater, and while VLC lets you do this, I don’t think YouTube does.

  15. Massaro permalink

    This is great, thank you very much! I’ve just watched the first few videos, and it seems that the whole series is a perfect “light” version of chapter 2 of your famous book.

    One small suggestion: I think it would be great if you devoted one or two videos for explaining things like the Heisenberg uncertainty principle and the no-cloning theorem, just like in the book. (Sorry if you’ve already done it, I haven’t watched all the videos yet).

  16. Thanks all for your kind words. I haven’t put them anywhere downloadable. I’ll look into doing so if I come back to complete the series.

  17. Steph W permalink

    Hi Michael,

    That’s great! Actually, we’ve been working on putting out some similar (although somewhat less introductory) series out, but it won’t be available until fall due to standard teaching constraints some of us have, so it’s great to have this intro!

    greetings from singapore,

  18. Toby permalink

    These are excellent, thanks a lot!

  19. Thank you!

    Is there any way you could put these up as videos for download (as opposed to just watchable within Youtube)? That would make them usable for people with limited Internet access, in presentation/classroom settings, etc.

    If bandwidth is a concern, Bittorrent is a good way to distribute using other people’s bandwidth.

  20. Suresh permalink

    Nice videos ! could you share with us the tech you used to make the videos ?

  21. Phys permalink

    Thank you, thank you and thank.. Great videos.. Really needed it.

  22. @Steph – great! Look forward to seeing them.

    @Suresh – The most important pieces were a Wacom Bamboo tablet, and Camtasia Screencast software. Camtasia is quite expensive, but I bought it cheaply from a friend who had won a copy in a competition, and didn’t want it. There’s probably low-cost or free alternatives available that do a similar job, but I haven’t investigated.

    I also used an Apex USB microphone, which I wasn’t very satisfied by.

  23. Nathaniel permalink

    I’ve just finished working through the videos, up to the unfinished postulates of quantum mechanics bit. (I got through them pretty quickly because I’ve been through Leonard Susskind’s online “quantum entanglements” course before, so your videos made a good mixture of revision and new information about the quantum computing perpective.) I’d be really happy to see the rest of the videos if you’re ever able to make them. In particular, it would be really nice to be taken through an example of an actual practical algorithm.

  24. @Nathaniel – Thanks for the feedback, I’ll definitely keep it in mind.

  25. Thank you for this really comprehensible course. I think it does a good job of “demestifying” quantum computations for those who are interested and ready to spend some time. Maybe it would make sense to number videos so that viewers could make sure that they follow the correct sequence, but it’s ok even without numbering.

  26. Oscar Cunningham permalink

    Thanks for the videos, you’re a great explainer. I’d love to see the rest of them if you ever have time to do them.

  27. Mircea Pricop permalink

    This is the first time I actually got a thorough understanding of quantum computing. Thanks a lot and I really really hope you will finish the series, especially the part about Grover’s.

  28. I second the idea of a torrent with all movies. Maybe on ?

  29. Johan Isaksson permalink

    Thank you very much for the videos!

    I have a question:
    Where you show the Hadamard gate connected to a cNOT gate you have two input qubits.
    They are combined into |00>. Can you separate them into two qubits (both of value |0>) and perform the same calculations? (with the same output) Is that even possible? If yes, how?


  30. Yes – the state |00> is just notational shorthand for |0>|0>.

  31. Johan permalink

    After the Hadamard gate, but before the cNOT we have:
    (|0> + |1>)/sqrt(2) as control
    |0> as target

    How are these represented with a vector which can be multiplied by the cNOT matrix?
    (a|00> + b|01> + c|10> + d|11>) the vector

    How do you go between the two vector representations? (2 separate 2-vectors and 1 combined 4-vector)

  32. The state with (|0>+|1)> as control and |0> as target is exactly the same as the state |00>+|10>. I’m omitting sqrt(2) factors, but, of course, they go out the front of everything.

  33. Johan Isaksson permalink

    I got it to work now. I used a tensor product of the two qubit vectors to create the length 4 vector. I need this since I am trying to write a software library for working with qubit gates as an exercise 😉

  34. Julio Cesar permalink

    Michael, I went through all videos and, man, please, whatever “work responsibilities that couldn’t be put aside” mean, finish the videos. Event better: record more of them! must say that Im even willing to pay to all the missing videos !

    Thanks for the great videos and Im hoping to get some more.


  35. Simon permalink


    Thanks for the videos – very illuminating.

    One question about quantum teleportation: If it’s impossible for Alice to know anything about the state of psi, how do she and Bob know that the experiment has worked? And hence how do we know the various real-world demonstrations of QT have actually worked? Or am I missing something obvious?


  36. For testing purposes we can imagine a third party, Tim, who prepares a state (which Tim knows, but Alice doesn’t), hands it to Alice, who then teleports it to Bob, who hands it back to Tim, who does tests to confirm that the teleported state is, indeed, the correct one.

    In practice, for testing purposes there’s really not much lost if you eliminate Tim, and Alice and Bob test by having Alice prepare known states to be teleported, which Bob then tests his final state against.

    One wrinkle in this is that in the final testing stage (whether done by Tim or Bob) it’s not possible to make a 100% accurate single-shot test that verifies that the right state has been teleported. (This is the problem you allude too: we can’t determine the state of an unknown quantum system.) So it’s necessary to repeat the experiment a large number of times, using a process called “state tomography” to gradually build up knowledge of what state is being teleported. The details of how state tomography works are a bit beyond this course, but I hope it’s at least plausible that this can be done.

  37. Zunaira permalink


    First of all I would like to thank you for such elaborate lectures. It has helped me a lot in understanding this subject area.
    I have a confusion regarding superdense coding. Suppose 2 qubits are entangled such that they have opposites spins. So, if 1st qubit is flipped, the 2nd will also undergoes a flip no matter how further apart they are. But this principle is not used in superdense coding. The 2 qubits are entangled, but despite the operations on the 1st qubit by Alice, 2nd qubit remains unchanged. Can you please explain why? doesnt this mean that we are denying the essence of entanglement?
    Looking forward to your response.

  38. @Zunaira: Your refer to the following as a ‘principle’: “Suppose 2 qubits are entangled such that they have opposites spins. So, if 1st qubit is flipped, the 2nd will also undergoes a flip no matter how further apart they are.”

    There is no such principle. Statements somewhat along these lines are sometimes made in some popular accounts, but those accounts are typically using vague and imprecise language to imperfectly capture something that is quite precise – the theory of quantum mechanics. Unfortunately, that makes it easy to arrive at misunderstandings based on those popular accounts.

  39. When are you going to record “The postulates of quantum mechanics IV”? I just watched the last available video last night. Great series. Thanks.

  40. @jackfoxy: As I said in the post, I have no immediate plans to complete the series.

  41. How embarrassing! I should have read your post instead of jumping straight to the videos.

  42. Anonymous Poster permalink

    Great work, please finish it!

  43. Axure permalink

    This is some awesome shit, dude!

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