Abstract
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.
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