Hilbert spaces (finite dimensional). Axioms of quantum probability. Quantum vs Classical probability.
Turing machines, Boolean circuits, Quantum Circuits, Universality. Simon's problem, Phase finding, Shor's algorithm, Grovers algorithm, Probability amplification. Some applications.
Quantum error correction.Knill-Laflamme theorem, Stabiliser codes
To be decided as the course progresses and if time permits.
Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press