An iterative approach for amplitude amplification with nonorthogonal measurements

TL;DR

This paper proposes an iterative amplitude-amplification method for integer factorization using coupled harmonic oscillators and non-orthogonal measurements, highlighting its potential and current resource limitations.

Contribution

It generalizes a previous amplitude-amplification method by incorporating non-orthogonal measurements, expanding the theoretical framework for quantum factorization techniques.

Findings

Method increases probability of finding factors

Requires exponential resources for implementation

Does not currently outperform classical algorithms

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.