An example depicting the power of quantum computing is [[Grover's algorithm]] for searching unstructured databases. The algorithm's quantum query complexity is <math display="inline">O{\left(\sqrt{N}\right)}</math>, a quadratic improvement over the best possible classical query complexity <math>\OmegaO(N)</math>, which is a [[linear search]]. While Grover's algorithm is more optimized than the best possible classical algorithm, we know that Grover's algorithm is not one hundred percent optimal.<ref>{{Cite journal|last=Ambainis|first=Andris|date=October 28, 2005|title=Polynomial degree vs. quantum query complexity|url=https://linkinghub.elsevier.com/retrieve/pii/S0022000005000899|journal=Journal of Computer and System Sciences|language=en|volume=72|issue=2|pages=220–238|doi=10.1016/j.jcss.2005.06.006|via=}}</ref> Optimization of a query algorithm refers to how the algorithm compares to the most efficient theoretical algorithm that solves the same problem. An algorithm is said to be [[Asymptotic optimality|asymptotically optimized]] if at worst, it performs at a constant factor worse than the most efficient possible algorithm. Note that an algorithm is still considered to be optimized if it performs worse than the most efficient possible algorithm, as long as the algorithm doesn't get exponentially worse than the most efficient possible algorithm, as the number of inputs increases.
