Syllabus
Theory of quantum computation is a relatively young field, however, its roots can already be found in the pioneering years of quantum mechanics and classical information theory. First the modern quantum information theory satisfactorily explained for example the Einstein-Podolsky-Rosen paradox or the Maxwell daemon. A spectacular success of this theory was the discovery of a polynomial quantum algorithm for number factoring by Shor, on the experimental field an equally important achievement was the realization of quantum teleportation. Entirely secure quantum cryptography, based on the fact that any eavesdropping on a transmitted quantum state is in fact a measurement and perturbes the state, is presently even commercially available and employed in military applications. Somewhat less medialized is the recent success on the field of quantum computations of many-body systems. The potential benefit of quantum computers for accurate calculations of many particle systems, which exhibit an exponential computational demands in the number of particles on classical computers, has been first realized by Feynman in 1982. In spring 2010 the first computation of the hydrogen molecule in minimal basis set has been published in Nature. In spite of the present limitation of quantum computers to a few qubits it is possible that a breakthrough in their scalability could come soon and they would thus become the technology of the 21st century.
Students interested in this lecture should master knowledge of quantum mechanics at least at the level of the course NOFY027 (Introduction to quantum mechanics).
The lecture is based partly on a selection of material from two textbooks (see Literature), partly on primary literature.
Selection of topics:
Reversible classical computations
Computational complexity
Quantum bit
Measurements in quantum mechanics
Entanglement, EPR and Bell inequalities
Quantum cryptography and teleportation
Quantum gates and circuits
Quantum Fourier transform
Shor's factoring algorithm
Quantum phase estimation algorithm and its iterative version
Quantum computations of many-electron systems
Quantum noise and error corrections codes
Alternatives of the gate model - adiabatic quantum computers
Annotation
This one-semester course is aimed for students interested in quantum computers, quantum algorithms and quantum information theory, with an accent towards their application to simulations of physical systems (cryptography topics will not be entirely dropped, but will not be in the central focus).