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Grover search is one of the most important quantum algorithms. In this paper,we consider a kind of search that the conditions of satisfaction $T$ can berewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search withsmaller oracles. The time complexity of this algorithm$O(\frac{\pi}{4}\sqrt{\frac{N}{b\lambda}}+\frac{\pi}{4}\sqrt{\frac{b}{\tau}})$,which is smaller than the time complexity of original Grover search, i.e.$O(\frac{\pi}{4}\sqrt{\frac{N}{M}})$.

Grover search with smaller oracles