Ferdinand Gleisberg | Searcharxiv

arXiv2022

Factorization with a logarithmic energy spectrum of a central potential

We propose a method to factor numbers based on two interacting bosonic atoms in a central potential where the single-particle spectrum depends logarithmically on the radial quantum numbers of the zero angular momentum states. The bosons initially prepared in the ground state are excited by a sinusoidally time-dependent interaction into a state characterized by the quantum numbers which represent the factors of a number encoded in the frequency of the perturbation. We also discuss the full single-particle spectrum and limitations of our method caused by decoherence.

quant-ph↗

arXiv2019

Prime Factorization of Arbitrary Integers with a Logarithmic Energy Spectrum

We propose an iterative scheme to factor numbers based on the quantum dynamics of an ensemble of interacting bosonic atoms stored in a trap where the single-particle energy spectrum depends logarithmically on the quantum number. When excited by a time-dependent interaction these atoms perform Rabi oscillations between the ground state and an energy state characteristic of the factors. The number to be factored is encoded into the frequency of the sinusoidally modulated interaction. We show that a measurement of the energy of the atoms at a time chosen at random yields the factors with probability one half. We conclude by discussing a protocol to obtain the desired prime factors employing a logarithmic energy spectrum which consists of prime numbers only.

quant-ph↗