00833nas a2200121   4500000000100000008004100001100001700042700002000059245002200079300001400101490000700115520058900122       2000                            d1 aJerzy Klamka1 aStefan Węgrzyn00aQuantum computing  a235–2460 v123 aIn the present studies on quantum computer systems principles of a quantum logic gates and basic elements of quantum computers are described. The fundamental elements of quantum computer and mathematical backgrounds of suitable quantum computation processes are presented. Specially Toffoli quantum gate and Hadamard quantum gate are discussed in details. Mathematical bases and principles of quantum computations are also mentioned. Finally, the role of nuclear magnetic resonance in quantum computations is investigated. Moreover, the extensive list of references is also presented.