# Quantum computing for the determined

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

- The qubit
- Tips for working with qubits
- Our first quantum gate: the quantum NOT gate
- The Hadamard gate
- Measuring a qubit
- General single-qubit gates
- Why unitaries are the only matrices which preserve length
- Examples of single-qubit quantum gates
- The controlled-NOT gate
- Universal quantum computation

### Superdense coding

- Superdense coding: how to send two bits using one qubit
- Preparing the Bell state
- What’s so special about entangled states anyway?
- Distinguishing quantum states
- Superdense coding redux: putting it all together

### Quantum teleportation

- Partial measurements
- Partial measurements in an arbitrary basis
- Quantum teleportation
- Quantum teleportation: discussion

### The postulates of quantum mechanics (TBC)

- The postulates of quantum mechanics I: states and state space
- The postulates of quantum mechanics II: dynamics
- The postulates of quantum mechanics III: measurement

*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.*

### Trackbacks and Pingbacks

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- Quantum Computing For The Determined – Michael Nielsen | SQLHack.net
- Quantum computing for the determined | Michael Nielsen | MP CyberBriefing
- A Brief History of Quantum Computing | wavewatching
- Quantum Computing for Dummies | Complex batch processing made simple
- Continuing Education: Quantum computing for the determined

Comments are closed.

This is really amazing and great, I hope you finish the remaining videos so we can have a complete course. It really is appreciated a lot.

I’ve not used linear algebra in depth (I’m a software developer) in over 16 years. I definitely would like to see the last 8 videos made, if you have the time!

You bring up the Khan Academy in the course and blog – have you considered working with him to make this one of his courses?

Want to join into the chorus and express my hope that you will find time to continue the video course. This is just a delightful introduction to QC. It is very instructive to see QM treated as abstracted mathematical framework for computational purposes. Inspired way to approach the subject.

I feel strongly this work should get about the same exposure as the better open courseware lectures on offer by MIT (i.e. viewership in the thousands rather than hundreds). To this end I took the liberty to submit a story to slashdot.org in order to promote this course.

Hopefully, this will gin up some viewership and maybe enough intellectually curious people will be sufficiently determined to make it through all videos.

@Henning – And Slashdot is exactly how I came across this. Thanks!

Thanks Michael! It’s been a decade since I did my senior level Quantum Mechanics course. Not sure if will be able to follow the lectures without brushing up the material, but I am hopeful. back in the days I used to follow the developments in Quantum Computing with great interest. With MIT’s 5 qbit quantum computer in Dec 2001(?) that did Shor’s algorithm and then the 7 qbit one. There was speculation that Quantum Computing was following Moore’s law. Then some how I lost track of it all (Job is a big killer). I heard of the Adiabatic one from D-Wave (or was it Q-Wave?). But feels like Q Computing has lost the momentum. Did it? Or is it just a lull before its going to come back in a big way?

Thanks for the lectures! And thanks to slashdot for bringing me here.

[MN: Thanks!]Thankyou all, for the nice words about my videos!

@Michael – I haven’t spoken with Khan. He’d certainly be welcome to integrate these into his Academy!

@Henning – Thanks for putting it on Slashdot!

I watched the first video and I can’t wait to watch the rest. I saw this story on slashdot. I hope you take these videos to the end. Quantum computing is an insane topic. Great job!

Great work! Here is another vote for you to finish the course!

Excellent series! Please complete the course when time allows.

Thanks for putting up these videos! It’s pretty interesting stuff. Initially thing were pretty simple, but I had a little trouble with the notation of at the superdense coding. So I tried to recreate it in matrix form to better understand what was happening. It turns out that my problem was two fold. First I hadn’t quite thought the consequences of the cNOT gate through, which has sunk in after reviewing the vids. But there’s still one result I can’t reproduce. In the video you give the result of the XZ operation as 10-11, but when I calculate it in matrix form I get (0 -1 1 0)/sqrt(2), or 10-01. Naturally I’d doubt myself first, but the latter makes much more ‘systematical’ sense. Could you verify if there is a mistake in the video of whether I should slap myself and start over again.

@Edwin: Thanks! As regards superdense coding, I simply made an error. See the comments on that video for more – someone else noticed the same thing, and commented there – but I’m pretty sure you got it right. (The fact you got it right strongly suggests you’re really understanding this well!)

Thanks! Rather silly to have missed that comment. But at least the road is clear to continue.

Many many thanks for these videos. I feel that there is so much more information conveyed through them than to simply read the information by itself.

I would love to see the course completed!

Excellent work!

A few years ago, I made it a goal to actually

understandQM before I die. (Rather than just oogle its mysteries from afar.) I’m an engineer, not a scientist, so am perfectly happy wallowing in linear algebra, probability, and complex numbers – and so I’m frustrated by popular articles on QM which cower away from that essential math, thereby explaining nothing, and leaving the theory looking like magic. Conversely, since I never had any advanced physics classes, I’m baffled by advanced scientific books presuming readers are already fluent with all the basic notation and elementary concepts of QM.A few rare resources, such as your videos, are aimed at exactly the right level: using the necessary math to construct the right mental models to create understanding. Thank you very much for building these bridges for me, and do please complete the rest of the set you had in mind!

@K Akella – Can’t pass up the opportunity to plug my own blog here. It’s purpose is to keep an eye on the evolving quantum computing industry and I just had an entry about how it’s prospects are undersold in the media: http://wavewatching.wordpress.com/2011/09/28/45/

Yet another vote to complete the video series, or at least “The postulates of quantum mechanics IV”

I just completed watching the video series (15 minutes is perfect for watching while on an exercise machine). Perhaps link to the script for the final chapter?

Thanks for a good job.

I am all for you completing this! Please do!!

Your great videos inspired me to try to explain come quantum phenomena to some math phobic colleagues in this series: http://mycodehere.blogspot.com/2011/11/quantum-computing-5-quantum.html (no ads) – but they boiled it down even further by making me remove most of the matrices, vectors and greek letters! I do hope that you complete this set, and also do something on algorithms?

Sir,

Its been great to study these lectures along with following your book. It would be great if you cud take some time off from your busy schedule and complete the series.

Please continue the course! I just started learning about quantum computation and this is a really good foundation. ðŸ™‚ I come from the wish to go deeper into quantum cryptography. I’m a cryptography student.

One more vote for more. I watched the 22 videos, and im curious how any algortihm might take advantage of the possiblities offered by the information in the state space.

I’ve just finished your videos and found them very helpful. So, I’d like to add another vote for finishing the course. (Looking forward to it!)

Thank you, gracias, shukran merci, toda.

Great job, and thank you for making it available.

Mauri.

Thanks very much. Superbly clear presentation. Another vote for the complete series.

Hello Sir, It was a pleasure watching this videos , hope you complete them . i am going for project on quantum computing for my masters in india , could you suggest some topics to simulate on standard computer for my project.

Also can you suggest some GUI based software in which we can simulate the simple quantum gates with single or multiple qbits so we can raise the complexity of the circuits , vary the inputs and observe the output of the gates . It would be real fun to build our custom circuits and do the calculations on paper and verify them on the simulator.

Sat down to watch the first video this morning, and now it’s gone 8 in the evening and I’ve finished them. I could easily have watched a few more. What a way to spend most of a Saturday! I loved the easy bite-sized chunks, and apart from a couple that were mostly proofs I enjoyed them all (sorry, I’m just not all that into proofs).

Great job.

Really looking forward to the next set when you get around to it!

Hi Michael,

You sound like you’re from Oz? I did a BSc in mathematical physics in Bert Green and Angus Hurst’s famous old dept in Adelaide many years ago (probably before your time) and have never entirely lost my interest, so I’ve seen the Hilbert space formulation before and solving the hydrogen atom, quantum scattering etc etc. Knew next to nothing about quantum computing.

I’ve seldom seen QM-related material explained so simply and clearly. Loved the lectures, any chance you will do more? Lec 22 just stops! And – if you don’t have time to write exercises, maybe a grad student might volunteer to write them?

Thanks,

Phil

PS: I like the way you basically put your notes, as you engage with a subject, on your blog. This pulls out the key points while laying out your reasoning or distillation process. It’s a good idea.

Definitely the best introduction i have seen. I thank people like Michael for lowering the bar for students of complicated “stuff” like this, thereby increasing the number of people that take us even further in our quest to understand the inner workings of nature. Go finish the videos when you have time Michael. Its greatly appriciated!

Shor’s algorithm, PLEASE, PLEASE!!!!!!!!!!!!!!!!!!!!!!!!

I would also like for you to finish the course.

Thank you very much for the great work you put in to make quantum computing understandable for every one through these video lectures.Looking forward for more such videos.

Thanks for the videos so far. +1 from me to complete them when you get some time. This was the only place I found the right level of detail for me. There was one thing that took me ages to understand. Assuming I now understand correctly! That was the fact that, for an N qubit system, you’d need 2 to the power N numbers to represent it’s internal state, and not 2 * N. Once I’d realised that, it all started to fall into place.

Sir, your videos are excellent. I regularly follow your book on Quantum Computation for my project works. It will be of immense help if you can manage some time and finish the course.

Hi, thanks for the videos, they’re really interesting ! Any chance on having some exercices to practice ?

Sir,

I am currently a first year undergraduate student of Electrical and Electronics engineering in India.

I don’t have an opportunity here to take courses on Quantum Mechanics, Information Theory, Algorithms, Complexity theory etc. I am interested in Quantum Computation and I want to do masters and Ph.D in this field.IS IT POSSIBLE?[Since I have no formal background of Physics, Math or Computer Science]