Several algorithms have been discovered which can be implemented on such devices  which run faster than the best known classical algorithms for the same problem. Among these are Grover’s algorithm (Grover 1996) for searching an unsorted database (which runs in time \(O(n^{1/2})\), whereas the best possible classical algorithm is \(O(n)\)) and Shor’s algorithm (Shor 1999) for integer factorization (which runs in \(O(\log_2(n)^3)\), whereas the best known classical algorithm is \(O(2^{\log_2(\log_2(n))^{1/3})}\)). Since it can be shown that quantum models can simulate models such as the classical Turing machine, \(\textbf{BQP}\) contains \(\textbf{P}\) and \(\textbf{BPP}\). And as we have just seen, \(\textbf{BQP}\) contains at least one problem – i.e. \(\sc{FACTORIZATION}\) – which is not known to be contained in \(\textbf{P}\).