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 supremacy
Quantum supremacy is the potential ability of quantum computing devices to solve problems that classical computers practically cannot. Quantum advantage is the potential to solve problems faster. In computational complexity-theoretic terms, this generally means providing a superpolynomial speedup over the best known or possible classical algorithm. The term was originally popularized by John Preskill but the concept of a quantum computational advantage, specifically for simulating quantum systems, dates back to Yuri Manin's (1980)
and Richard Feynman's (1981) proposals of quantum computing.