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Fakultät für Mathematik Universität Regensburg
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Introduction to the Mathematics of Quantum Computing
SoSe 2023

Florian Strunk

Type of course (Veranstaltungsart)

German title
Einführung in die Mathematik des Quantum Computing


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 non-binary 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
  • No-cloning theorem vs. quantum teleportation
  • Holevo's bound vs. dense coding
  • Deutsch-Jozsa 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

  • 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

Tue 10-12


Additional question session
Time/Date: Wed 14-16
Location: M101

Course homepage
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

  • 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, re-exam: Date: individually