In recent years, the relatively new field of quantum information processing (QIP) has attracted the attention of many scientists around the world due to its promise of increased computational speed, absolute secure communication and the potential to simulate complex quantum mechanical systems. The very essence of this new quantum information technology are two concepts at the very heart of quantum mechanics, namely superposition and entanglement. The present Thesis contains the results of four

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... ifferent experiments that were all aimed at the demonstration of an entirely new model for quantum computing with linear optics --- the "one-way" quantum computer. For this purpose a multi-photon entangled state of four photons has been generated via the process of spontaneous parametric down-conversion and by using an interferometric setup. This entangled state acts as a resource that allowed for novel demonstrations of quantum algorithms and relevant experimental techniques. By exploiting the advances developed in both theory and experiment, in this Thesis we report the implementation of fast, active feed-forward that allowed, for the first time, the realization of deterministic linear-optics quantum computing at an unprecedented speed. Further we were able to demonstrate the Deutsch algorithm on our one-way quantum computer, an important quantum algorithm that is capable of distinguishing whether a function is constant or balanced. Classically one needs to query the algorithm at least $2^{N-1}+1$ times for an N-bit binary input string, however, in the quantum regime, this can be done with one evaluation of the algorithm, independent of the size of the input. In another experiment we succeeded in playing an instance of a quantum game --- the so-called Prisoner's dilemma --- on our one-way quantum computer. Playing such a game is essentially the execution of a quantum algorithm made up of a distinct set of one- and two-qubit gates. This allows the individual players to increase their strategy space, as they can also choos [...]