Shor’s prime
factorization algorithm is one of the most important quantum algorithms, and it
also serves as a benchmark to characterize quantum computation performance. The
prime factorization algorithm has been implemented by different physical
approaches with various conditions on scalability level. Quantum teleportation,
quantum Fourier transform, quantum key distribution, quantum communication
protocols, and quantum error-correction methods – which are not computational
problems, however – play a crucial role in the realization of distributed
quantum computations. Their practical implementations are essential for any
future experimental quantum computations, such as the development of the
quantum Internet. Some practically implemented quantum algorithms belong to the
quantum machine learning field. Quantum programming languages are also a distinct
field with the purpose of developing appropriate programming languages for
quantum computers.
