  Using three coupled harmonic oscillators, we present an
amplitude-amplification method for factorization of an integer. We generalize
the method in [arXiv:1007.4338] by employing non-orthogonal measurements on the
harmonic oscillator. This method can increase the probability of obtaining the
factors by repeatedly using the nonlinear interactions between the oscillators
and non-orthogonal measurements. However, this approach requires an exponential
amount of resources for implementation. Thus, this method cannot provide a
speed-up over classical algorithms unless its limitations are resolved.
