The main aim of this work is to investigate manifestations and properties of the deterministic chaos phenomenon in quantum mechanical systems as well as to study their stability using the mathematical apparatus of quantum chromodynamics. Approaches to generalize the notion of chaos in the case of quantum fields are also analyzed. A brief review of deterministic chaos theory for classical Hamiltonian systems is made. We propose original chaos criterion for quantum field systems which is formulated in the framework of path integral formalism. Its correspondence with classical chaos criteria is demonstrated in semiclassical approximation of nonrelativistic quantum mechanics. Exploiting mathematical analogy between Wilson loop introduced in quantum chromo\-dynamics and the definition of fidelity, a quantity defining the stability of quantum system - the stability of holonomic quantum computations - is studied in the generic case with respect to uncontrollable errors in assignment of the classical control parameters. In the framework of the instanton approach some dynamical tunneling process properties are analytically calculated for one-dimensional model quantum mechanical system affected by perturbation periodic in time. It is shown that the results obtained are in agreement with the results of the independent numerical simulations. In connection with the question about the role of deterministic chaos in elementary particle physics, the main works dedicated to the investigation of the classical gauge fields chaotic dynamics are briefly discussed. The transition from the regular to chaotic motion at the interaction between Yang-Mills fields and classical vacuum Higgs field is also considered. The influence of quantum fluctuations on the critical density of energy corresponding to such a transition is studied in the case of nonvacuum Higgs field considered as a dynamical degree of freedom.

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