Jose Luis Rosales & Vicente Martin.
Quantum simulation of the integer factorization problem: Bell states in a Penning trap, Physical Review A (2018). DOI: 10.1103/PhysRevA.97.032325, arXiv: 1704.03174
>The arithmetic problem of factoring an integer N can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of N, are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of N. This is equivalent to a quantum sieve that is shown to require only o(ln√N)³ energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.
tl;dr or tt;du (too technical; didn't understand): we can estimate which prime factors are more likely using a quantum simulator, and this is a workaround for breaking RSA encryption which is based exactly on the computational difficulty of that problem to classical methods.