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 algorithm for linear systems of equations
In June 2018, Zhao et al. developed an algorithm for performing Bayesian training of deep neural networks in quantum computers with an exponential speedup over classical training due to the use of the quantum algorithm for linear systems of equations, providing also the first general-purpose implementation of the algorithm to be run in cloud-based quantum computers.