Factorization with a logarithmic energy spectrum of a two-dimensional potential

We propose a method to factor numbers using a single particle caught in a separable two-dimensional potential with a logarithmic energy spectrum. The particle initially prepared in the ground state is excited with high probability by a sinusoidally time-dependent perturbation into a state whose two quantum numbers represent the factors of a number encoded in the frequency of the perturbation. We discuss the limitations of our method arising from off-resonant transitions and from decoherence. - Highlights: • A new protocol for factorization of an integer into two primes is proposed. • We report an energy spectrum optimally adapted for the factorization. • A potential for our single particle spectrum was calculated numerically. • We determined a Rabi frequency for the transition into the factor state. • An explicit limit caused by decoherence for numbers to be factored is reported