# Theory @ Tartu

### Theoretical Computer Science

### University of Tartu

## How to study

# Quantum Computing

How about that: There's a topic on which physicists, engineers, bankers, and politicians are all in agreement: Quantum computers are only a few years away from kicking off a revolution into which countries and companies are investing billions of Euros, Dollars (US, Canadian, Australian), Yuan, Pounds, Kronen, ...

What can quantum computers do so much better than "classical" computers? How can I make quantum computers do things?

Quantum computing isn't about running algorithms on a new hardware platform. Microsoft researcher Matthias Troyer says: *"There's been no change in the way we compute since the last 5000 years. And now is the time when this is changing. Because with quantum computing, we are radically changing the way we use nature to compute."* (YouTube)

Quantum computing exploits the arcane laws of quantum mechanics. Albert Einstein referred to quantum mechanics as "black magic calculus" — take that as an indication that it takes some "getting used to". At the University of Tartu, we are offering a carefully thought through list of courses in "quantum sorcery".

### 1st Semester: Mathematical Foundations

Quantum mechanics is a mathematical language to describe states of and operations on systems, such as a qubit or the whole quantum computer. Making sense of quantum algorithms and programming quantum computers requires a thorough understanding of the underlying math. There's no way around this. The course **MTAT.05.008 Foundations of Mathematics** starts by reviewing basic undergraduate math (vector spaces, bases, linear mappings, matrices, ...), and takes you through complex numbers, spectral theorems, and the infamous Dirac Notation all the way to pure quantum states (which are just vectors, really) mixed quantum states (which are just matrices, really), quantum operations (unitary matrices) and measurement (also matrices in a way).

You may want to consider taking the **Quantum Seminar** in the 1st semester — just for fun.

### 2nd Semester: Quantum Computing & Quantum Crypto

Having suffered through MTAT.05.008, you're ready to cash in. In **MTAT.07.024 Quantum Crypto** you learn how to use quantum stuff for secure communication, e.g., quantum key distribution and variants. As a design choice, the content in the first 4 weeks of MTAT.07.024 overlaps heavily with the last weeks of MTAT.05.008: This shit is hard, and working through it twice will help you understand it.

In **MTAT.05.118 Quantum Computing** you learn the basic quantum algorithms, including the famous Grover search and Shor's factoring algorithm which breaks RSA encryption.

What about another Quantum Seminar, or a **quantum-computing related company project**?

### 3rd Semester: Big Project

Time to put into action what you have learned: The 12 credit point **Research Project** gives you that opportunity, while at the same time preparing you for your master's thesis. Start the work in the summer between 2nd and 3rd semester, write down a short report for the research project at the end of the 3rd semester, and bash on relentless with your master's thesis in the 4th semester.

- AI? Wanna code a quantum neural network? Or a Gibbs sampler for a Boltzman machine? Work out a hybrid quantum-classical deep learning architecture? Let's do it! (Note: You need to take LTAT.02.001 Neural Networks in the 2nd semester, and ideally also a seminar on advanced neural network architectures.)
- Programming languages, compilers? Contribute in an ongoing project to develop a kick-ass open source quantum compiler — because the quantum revolution belongs to everyone, not just Microsoft/IBM/Google.
- Or are you a true theorist? Maybe design a new quantum algorithm? Work out the best quantum circuits for a particularly important sub-task? Let's talk about it!

You may want to consider taking one of the additional courses in quantum computing, e.g., **MTAT.05.123 Advanced Quantum Algorithms**.

### 4th Semester: Master's Thesis

Finish it, write it, defend it, celebrate it. Pick your employer, enjoy your quantum computing career. Or, continue with a PhD, because there's so much more that needs to be done!