A New Quantum Algorithm in Case of a Special Function (New Version)
Koji Nagata, Tadao Nakamura, Han J.F. Geurdes, Ahmed Farouk, Josep Amengual i Batle, S. Abdalla, Germano Resconi · viXra · 2017
We present a new quantum algorithm. It determines the property of a function. It is $f(x)=f(-x)$. How fast can we succeed? The quantum algorithm does not use the Hadamard transformation. All we need is of evaluating $|\overbrace{0,0,...,1}^N\rangle$. And we can know the global property, that is, we can realize $f(x)=f(-x)$ for numbers. Our quantum algorithm overcomes a classical counterpart by a factor of $O(2^N)$.