| Shor's algorithm for factoring large numbers into their primes, Grover's search algorithm and other powerful algorithms initiated significant theoretical and experimental work in quantum computing. The algorithms were based on simple unitary transformations. The foundations of which were proposed by Feynmann and Deutsch in the eighties. The primary thrust of most researchers is to find physical systems in which these unitary evolutions might be realized. However, decoherence and the inability to scale have prevented rapid experimental progress in the field.;The primary thrust of this thesis is based on the use of single-photon interferometry in linear optics and linear integrated optics. It has been shown that single-photon interferometry can simulate the unitary evolutions of quantum computing. Unfortunately, apparata using linear and linear integrated optics scale poorly. This is due to the fact that each degree of freedom of the single-photon represents a basis state. Hence, the apparatus grows with the Hilbert space, which grows exponentially with the number of bits. However, these linear environments have relatively small decoherence and high repeatability. In addition, weak classical fields can be used as the sources. Hence, the environment is especially useful and (relatively speaking) simple for small-bit applications. Several few-bit circuits will be studied using linear and linear integrated optics circuits.;Some discussion will also be given to using entangled photons in quantum circuits. Entangled photons have an advantage in that the apparatus size scales with the number of photons instead of with the Hilbert space. The difficulty with using entangled photons is that it is nontrivial to generate, manage and detect single photons. |
