Even if P ⊊ BQP were proven, further empirical investigation would be required to determine quantum computation's bearing on feasible computation or the Cobham-Edmonds thesis

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