Simpler quantum counting
(pp0967-0983)
Chu-Ryang
Wie
doi:
https://doi.org/10.26421/QIC19.11-12-5
Abstracts:
A simpler quantum counting algorithm based on amplitude
amplification is presented. This algorithm is bounded by O(sqrt(N/M))
calls to the controlled-Grover operator where M is the number of marked
states and N is the total number of states in the search space. This
algorithm terminates within log(sqrt(N/M)) consecutive measurement steps
when the probability p1 of measuring the state |1> is at least 0.5, and
the result from the final step is used in estimating M by a classical
post processing. The purpose of controlled-Grover iteration is to
increase the probability p1. This algorithm requires less quantum
resources in terms of the width and depth of the quantum circuit,
produces a more accurate estimate of M, and runs significantly faster
than the phase estimation-based quantum counting algorithm when the
ratio M/N is small. We compare the two quantum counting algorithms by
simulating various cases with a different M/N ratio, such as M/N > 0.125
or M/N < 0.001.
Key words:
quantum counting, Hadamard test, amplitude amplification,
simulation |