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

•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.

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.