Integrated quantum photonics
As the field has progressed new quantum algorithms have been developed which provide short and long term routes towards the demonstration of the superiority of quantum computers over their classical counterparts. Cluster state computation is now generally accepted as the approach that will be used to develop a fully fledged quantum computer. Whilst development of quantum computer will require the synthesis of many different aspects of integrated optics, boson sampling seeks to demonstrate the power of quantum computation via technologies readily available and is therefore a very promising near term algorithm to doing so. In fact shortly after its proposal there were several small scale experimental demonstrations of the boson sampling algorithm
Topological quantum computer
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball (representing an ordinary quantum particle in four-dimensional spacetime) bumping into a wall. Alexei Kitaev proposed topological quantum computation in 1997. While the elements of a topological quantum computer originate in a purely mathematical realm, experiments in fractional quantum Hall systems indicate these elements may be created in the real world using semiconductors made of gallium arsenide at a temperature of near absolute zero and subjected to strong magnetic fields.