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
Quantum computing
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely. For some problems, quantum computers offer a polynomial speedup. The most well-known example of this is "quantum database search", which can be solved by Grover's algorithm using quadratically fewer queries to the database than that are required by classical algorithms. In this case, the advantage is not only provable but also optimal, it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.