Physics – Quantum Physics
Scientific paper
2010-10-19
Physics
Quantum Physics
35 pages, 9 figures
Scientific paper
Using three coupled harmonic oscillators, we have recently proposed [arXiv:1007.4338] an alternative approach for quantum factorization of an integer. However, the probability of obtaining the factors becomes low when this number is large. Here, we circumvent this limitation by using a new iterative method which can efficiently increase the probability of finding the factors. We show that the factors of a number can be obtained, in linear time, with a high probability. This amplitude-amplification method can be applied to search problems. This implies that search-based problems including NP-complete problems can be exponentially sped up. In addition, we generalize the method of amplitude amplification by using a system of coupled harmonic oscillators. This can be used for solving a system of linear or nonlinear functions with integer inputs subject to a number of constraints. The total number of oscillators in the system is equal to the number of integer variables in the functions plus the number of constraints.
Ng Hwee Tou
Nori Franco
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