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Abstract

This thesis proposes an interactive quantum computer simulator to improve the understanding of the power and limitations of quantum computers.

Quantum computers changed the paradigm of theoretical computer science that complexity classes of computable problems are the same throughout all possible computer architectures. Indeed, it has been proven that there exist efficient quantum algorithms for problems that are intractable on any classical universal Turing machine. Since the experimental realization of a reasonably sized quantum computers
is beyond today's capacities, simulations are the only way to verify theoretical predictions.

The presented program is suited to design, test and visualize quantum algorithms with up to 20 qubits on commonly available personal computers. It incorporates the simulation of operational and decoherence errors for them being of critical importance for the feasibility of quantum computations.

The use of the simulator is demonstrated with the help of a quantum algorithm for obtaining eigenvalues and eigenvectors of a Hamiltonian, and threshold values for successful quantum computations in the presence of errors are calculated and compared to previous scientific works.