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 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: 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
- 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
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.