Linear optics quantum computing – construction of small networks and asymptotic scaling

In the paradigm of linear optics, quantum states of optical field modes are manipulated by means of photon sources, beam splitters, and photodetectors. This restriction of the allowed interactions introduces non-unit success probabilities into every non-trivial computation irrevocably. The resulting probabilistic nature of this architecture opens up questions about scalability of this approach as well as about basic limitations like optimal resource consumption and the construction of optical networks for given tasks. The scalability question is addressed within the framework of cluster state computing which allows to shift the problem towards the problem of scalable state production. Several schemes with different constraints, resulting in different experimental feasibility, are shown to exhibit optimal scaling behaviour. These schemes include restrictions to certain easy-to-implement gate sets, and the banning of re-routing, which is a major obstacle in optical quantum computing. In the small-scale regime various methods for constructing and analysing linear optics networks are presented. Rather than constructing the gates in the general quantum gate model, a direct construction from linear optics’ basic elements – beam splitters and phase shifters – will be considered. This can result in higher success probabilities and smaller resource consumption. Due to the complexity of the problems, these techniques are applicable only to quantum gates which involve a small number of optical modes and photons. A couple of examples ranging from state preparation over quantum gates to state discrimination are used to illustrate these tools. LOQC – construction of small networks and asymptotic scaling 2