Module 10! Can you believe it – you made it till the end! We’re certainly impressed: it’s been quite a tough course. But you put in a lot of work, and learned a lot. So for the last module we decided to give you (and ourselves :-)) a break. We’d like to tell you about some of our favorite topics in quantum cryptography, that we didn’t have a chance to cover in detail in the amount of time we had.

The first topic is position-based cryptography. Suppose Alice and Bob want to prove to Charlie that they are located at two distinct places on the globe – say Alice is in Delft, and Bob in Pasadena. Can they do it? Using quantum information, and a tiny bit of relativistic mechanics, they can! We’ll show you how in 10.1.

The second topic concerns the problem of delegating quantum computations. Alice has a quantum circuit she wants to implement, for example Shor’s quantum algorithm for factoring. But she doesn’t have a quantum computer. IBM (or, “the cloud”) has a quantum computer, and they’re willing to sell computation time to Alice. But Alice might not trust the cloud: given she cannot perform the computation herself, can she still verify it? In 10.2 we’ll give a general introduction to this problem, and in 10.3, 10.4 and 10.5 we’ll present three different methods to implement delegated computation. As you’ll see, none of the methods is fully satisfactory, but each has some very interesting ideas.

Finally, don’t forget to join us in 10.6 for a last goodbye and a whirlwind tour of yet other exciting topics we really had not time to discuss – but we encourage you to explore on your own!

Before you head off, be warned that the material in this week is somewhat more advanced than in previous weeks. Our goal was to survey some exciting topics, giving you a good idea of the research while not delving too much into the detail. In particular, the lecture notes contain a fairly detailed exposition of delegated computation, but they are meant for your curiosity only: the material is not mandatory, so you should not worry if you can’t follow the whole discussion there. In a similar vein, we included an optional homework section walking you through the model of measurement-based quantum computation. We are certain you will enjoy working through these problems, but you do not need to: they will not be graded. (Watch that the two “regular” problems in the “Homework” section *will* be graded!)