To provide a quantum computation method for solving such a problem that, when an unknown function with invariance of f(x)=f(xΛs) or g(x)=g(xVs) and Hamming weight of an n-bit column s are given, an appropriate input value is inputted to the function and the s is found out as the output value of the function.
The quantum computation method includes the steps of: initializing all the qubit of first and second registers each composed of n pieces of two-state systems; making Hadamard transform act on the first register and constituting a uniform overlap state; and making unitary transformation act on the first and second registers thereby generating such quantum entanglement that the second register becomes |f(x)> or |g(x)> when the first register is |x> between the two registers, making the Hadamard transform act on the first register again, observing the first register by a base {|x>: x belonging to a set {0,1}n}, and finding out the s from the observed value.
Shiro Takayanagi
Yasuhiro Otsuka
Shuji Kimura