1301.4461 (K. Uyanik et al.)

Sure-Success Quantum Algorithms on Weight Decision Problem    [PDF]

K. Uyanik, S. Turgut

Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single variable. For problems that require a large number of iterations, it is observed that the iteration number of sure-success quantum algorithms scale as the square root of the iteration number of the corresponding classical probabilistic algorithms. It is also demonstrated that for a few iterations, quantum algorithms can be more efficient than this.

View original: http://arxiv.org/abs/1301.4461