  Recently developed quantum algorithms suggest that quantum computers can
solve certain problems and perform certain tasks more efficiently than
conventional computers. Among other reasons, this is due to the possibility of
creating non-classical correlations, or quantum entanglement, which is a
phenomena hard or impossible to reproduce by classical-information methods.
  In this thesis I first investigate the simulation of quantum systems on a
quantum computer constructed of two-level quantum elements or qubits. For this
purpose, I present algebra mappings that allow one to obtain physical
properties and compute correlation functions of fermionic, anyonic, and bosonic
systems with such a computer. The results obtained show that the complexity of
preparing a quantum state which contains the desired information for the
computation is crucial.
  Second, I present a wide class of quantum computations, which could involve
entangled states, that can be simulated with the same efficiency on both types
of computers. The notion of generalized quantum entanglement then naturally
emerges. This generalization of entanglement is based on the idea that
entanglement is an observer-dependent concept, that is, relative to a set of
preferred observables.
