1 research outputs found
Error reduction of quantum algorithms
We give a technique to reduce the error probability of quantum algorithms
that determine whether its input has a specified property of interest. The
standard process of reducing this error is statistical processing of the
results of multiple independent executions of an algorithm. Denoting by
an upper bound of this probability (wlog., assume ),
classical techniques require executions
to reduce the error to a negligible constant. We investigated when and how
quantum algorithmic techniques like amplitude amplification and estimation may
reduce the number of executions. On one hand, the former idea does not directly
benefit algorithms that can err on both yes and no answers and the number of
executions in the latter approach is . We propose
a novel approach named as {\em Amplitude Separation} that combines both these
approaches and achieves executions
that betters existing approaches when the errors are high.
In the Multiple-Weight Decision Problem, the input is an -bit Boolean
function given as a black-box and the objective is to determine the
number of for which , denoted as , given some possible
values for . When our technique is applied to
this problem, we obtain the correct answer, maybe with a negligible error,
using calls to that shows a quadratic speedup
over classical approaches and currently known quantum algorithms