  We propose an algorithm using a modified variant of amplitude amplification
to solve combinatorial optimization problems via the use of a subdivided phase
oracle. Instead of dividing input states into two groups and shifting the phase
equally for all states within the same group, the subdivided phase oracle
changes the phase of each input state uniquely in proportion to their objective
value. We provide visualization of how amplitudes change after each iteration
of applying the subdivided phase oracle followed by conventional Grover
diffusion in the complex plane. We then show via numerical simulation that for
normal, skew normal, and exponential distribution of objective values, the
algorithm can be used to amplify the probability of measuring the optimal
solution to a significant degree independent of the search space size. In the
case of skew normal and exponential distributions, this probability can be
amplified to be close to unity, making our algorithm near deterministic. We
then modify our algorithm in order to demonstrate how it can be extended to a
broader set of objective value distributions. Finally, we discuss the speedup
compared to classical schemes using the query complexity model, and show that
our algorithm offers a significant advantage over these classical approaches.
