algorithm oracle Hamiltonian oracle model
A well studied formula is the balanced binary tree with only NAND gates. This type of formula requires Θ(N) queries using randomness, where 



c
=

log

2


⁡
(
1
+


33


)

/

4
≈
0.754


{\displaystyle c=\log _{2}(1+{\sqrt {33}})/4\approx 0.754}

. With a quantum algorithm however, it can be solved in Θ(N) queries. No better quantum algorithm for this case was known until one was found for the unconventional Hamiltonian oracle model. The same result for the standard setting soon followed.
