Structured quantum search in NP-complete problems using the cumulative density of states

الأصل · EN

In the multitarget Grover algorithm, we are given an unstructured N-element list of objects Sᵢ containing a T-element subset tau and function f, called an oracle, such that f(Sᵢ)=1 if Sᵢ is in tau, otherwise f(Sᵢ) = 0. By using quantum parallelism, an element of tau can be retrieved in O(sqrt(N/T)) steps, compared to O(N/T) for any classical algorithm. It is shown here that in combinatorial optimization problems with N=4ᵐ, the density of states can be used in conjunction with the multitarget Grover algorithm to construct a sequence of oracles that structure the search so that the optimum state is obtained with certainty in O(log(N)) steps.