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Bounds on quantum ordered searching
Peter Hoyer, Jan Neerbek
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}π(\ln(N)-1) queries to the list. This improves upon the previously best…
Quantum Algorithms for Element Distinctness
Harry Buhrman, Christoph Durr, Mark Heiligman +4
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, H…
On Arbitrary Phases in Quantum Amplitude Amplification
Peter Hoyer
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplificat…
Quantum Amplitude Amplification and Estimation
Gilles Brassard, Peter Hoyer, Michele Mosca +1
Consider a Boolean function that partitions set between its good and bad elements, where is good if and bad otherwise. Consider also a quantum a…