**Prerequisites**

Familiarity with basic linear algebra, probability theory, discrete math, algorithms, all at the level of a first Bachelor's course. Also general mathematical maturity: knowing how to write down a proof properly and completely.

**Aim of the course**

Today's computers---both in theory (Turing machines) and practice (PCs and smart phones)---are based on classical physics. However, modern quantum physics tells us that the world behaves quite differently. A quantum system can be in a superposition of many different states at the same time, and can exhibit interference effects during the course of its evolution. Moreover, spatially separated quantum systems may be entangled with each other and operations may have ``non-local'' effects because of this. Quantum computation is the field that investigates the computational power and other properties of computers based on quantum-mechanical principles. Its main building block is the qubit which, unlike classical bits, can take both values 0 and 1 at the same time, and hence affords a certain kind of parallelism. The laws of quantum mechanics constrain how we can perform computational operations on these qubits, and thus determine how efficiently we can solve a certain computational problem. Quantum computers generalize classical ones and hence are at least as efficient. However, the real aim is to find computational problems where a quantum computer is much more efficient than classical computers. For example, Peter Shor in 1994 found a quantum algorithm that can efficiently factor large integers into their prime factors. This problem is generally believed to take exponential time on even the best classical computers, and its assumed hardness forms the basis of much of modern cryptography (particularly the widespread RSA system). Shor's algorithm breaks all such cryptography. A second important quantum algorithm is Grover's search algorithm, which searches through an unordered search space quadratically faster than is possible classically. In addition to such algorithms, there is a plethora of other applications: quantum cryptography, quantum communication, simulation of physical systems, and many others. The course is taught from a mathematical and theoretical computer science perspective, but should be accessible for physicists as well.

**Lecturers**

Ronald de Wolf (CWI and ILLC)

TA: Lynn Engelberts, Daan Schoneveld, and Quinten Tupker (CWI/UvA)

**Video recordings**

This year's lecture won't be recorded because Mastermath has only a limited number of cameras available. Instead, for the first 14 lectures you can watch the video's from the 2022 version of this course, which are at

https://vimeo.com/showcase/9241142 with password 98rT

For the 15th lecture (quantum error-correction) unfortunately there's no old video available.

**Rules about Homework/Exam**

Your final grade will be determined 40% by homework and 60% by a final 3-hour exam in June (with the possibility of a re-sit of the exam a few weeks later). It's a general rule of Mastermath courses that you need an exam grade of at least 5.0 and a final grade of at least 5.5 to pass the course. Also, the final grade will be rounded to the nearest integer.

There will be 7 homework sets. You can write down your solutions, scan them (for instance using an app on your phone), and upload them as one pdf file on the ELO website before the deadline via the "Homework" assignments that I will set up there. Your homework grade will be determined by the best 6 of your 7 homework grades, so no big problem if you mess up or skip 1 of the homeworks. This also covers cases where you might not be able to hand in a particular homework set on time for whatever reason, so please don't ask me for permission to submit late.

Homework still counts as part of the grade after retake

**Lecture Notes/Literature**

https://homepages.cwi.nl/~rdewolf/qc24.html

- Docent: Ronald de Wolf