LTAT.04.008
Introduction to
Quantum Algorithms
Course overview
The course covers the basic techniques in and examples of quantum algorithms.
Building on top of the course LTFY.04.012 Fundamentals of Quantum Computing (FunQ), we start with a crash review of basic quantum mechanics, and then move to discuss the quantum circuit model of universal quantum computation. We'll swoop up some quantum computational complexity theory, as tourists.
Then we'll be ready for the quantum algorithms:
- Quantum Fourier Transform
- Quantum Phase Estimation
- Quantum Amplitude Amplification
- Quantum Amplitude Estimation.
These algorithms stand for the basic techniques; we will see a few more examples based on them: Schor's (quickly: it's covered in depth in MTAT.07.024 Quantum Crypto), Deutsch-Josza, Bernstein-Vazirani, Simon's.
The techniques/algorithms are covered in their simplest but abstract versions: For example, we cover the "abstract" version of Grover (namely QAA), but we don't spend much time on the important variants of QAA (robust, oblivious).
With that, the emphasis of the course is not on the ability to write down quantum circuit diagrams for many simple quantum algorithms but on the mathematics that makes the algorithms work.
Required background
- FunQ: Hilbert space, Dirac notation, orthonormal bases, operators, projectors; measurement; composite systems and tensor products; quantum circuits and gates.
The course relies heavily on finite-dimensional Hilbert space, along with spectral theory and tensor products, including Dirac notation. We will not review that material.
👉 It is recommended to take MTAT.07.024 Quantum Crypto in parallel with Quantum Algorithms.
Organization
The course consists of:
- Wed 14-16, Delta 2034: Lecture session
- Fri 14-16, Delta 2047(+1024?): Discussion (or "practice") session
- Independent study and homework assignments
Lectures. The lectures are based on slides, which will be made available to the students, plus examples, calculations, and proofs on the whiteboard. Attendance is mandatory.
Practice sessions. In the practice sessions we will address students' questions about the lecture content and the homework assignments. Based on the speed at which the lectures proceed (depends on the audience), some lecture material may spill into the practice sessions.
Homework assignments are "theory" only, meaning, no programming or so. Frequency: One HWA in 2 weeks.
Learning Environment. We use a (private) GitHub repository for making the slides and homework assignments available to the course participants. Not yet online: github.com/dojt/qualms2023.
Course grade. final_exam == false
Participants are assumed to be self motivated to reviewing the material continuously (as opposed to being motivated by exam angst and reviewing on the day before the exam). The course grade is the average of the homework assignment marks.
Team
- Assoc. Prof. Dirk Oliver Theis: Content, organization, practice sessions.
- Evgenii Dolzhkov: Lecture sessions.