Introduction to the Mathematics of Quantum Computing Semester SoSe 2023
Lecturer Florian Strunk
Type of course (Veranstaltungsart) Vorlesung
German title Einführung in die Mathematik des Quantum Computing
Contents
This (2SWS) lecture course is a basic and concise introduction to the mathematics of quantum computing.
Quantum computing is a type of computation whose operations use phenomena of quantum mechanics.
Even though devices that perform these quantum computations  i.e. quantum computers  exist, at the moment, only very limited in size, an associated theory of computation is well established and precise.
Just as a bit (0 or 1) is a fundamental unit of classical computation, a qubit (a unit vector in the complex ℂ^2) is a fundamental unit of quantum computation.
(Think of the classical bits as (1,0) and (0,1).)
A system of such qubits, a quantum state, can be modified by quantum logic gates, e.g. NOT, AND, OR, which are just certain unitary matrices.
In contrast to the classical situation, there are "more" operations one can perform.
Systems of such quantum gates (and more), are called quantum circuits.
Just as in the classical setting (with just 0 and 1), one may model elementary arithmetic operations by these circuits and ask about benefits in complexity.
In the lecture, we will explore the language of this nonbinary world and study some fundamental problems.
Here is a list of topics (most likely) treated in the lecture:
 Qubits and entangled states
 Quantum logic gates and quantum circuits
 Toffoli gate and universality
 Quantum circuits for elementary arithmetic operations
 Nocloning theorem vs. quantum teleportation
 Holevo's bound vs. dense coding
 DeutschJozsa algorithm
 Grover's search algorithm
 Quantum Fourier transformation (and arithmetic addition revisited)
 Shor's factorization algorithm and consequences for cryprography
 Recollection of complexity theory: Turing machines and the classes P and NP (if time permits)
 Quantum complexity theory: Quantum Turing machines the classes BQP and QMA (if time permits)
There will be a weekly tutorial in which we try so solve exercises accompanying the lecture.
(There will be no homework to be handed in.)
If all participants agree, this course can be held in German
Literature
 Burkhard Lenze  Mathematik und Quantum Computing
 Kurgalin, Borzunov  Concise Guide to Quantum Computing
 Nielsen, Chuang  Quantum Computation and Quantum Information
 Scherer  Mathematics of Quantum Computing
 Scherer  Mathematik der Quanteninformatik
 Bernstein, Vazirani  Quantum complexity theory
 Vazirani  A survey of quantum complexity theory
Recommended previous knowledge Linear Algebra
Time/Date Tue 1012
Location M104
Additional question session Time/Date: Wed 1416 Location: M101
Course homepage https://elearning.uniregensburg.de/course/view.php?id=60077 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)
Registration Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen) Oral examination (without grade): Duration: 30, Date: individually
Examination (Prüfungsleistungen) Oral exam: Duration: 30, Date: individually, reexam: Date: individually
Modules BV, MV
ECTS 3
