Prime factorization using coupled oscillators with positive feedback

Abstract

Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. In this work, we describe an approach to prime factorization using coupled oscillators with positive feedback. The approach includes several steps, where some of the steps are accomplished on a general type computer, and some steps are accomplished using coupled oscillators. We present experimental data on finding the primes of N = 817. The experiment is performed on a system of two coupled active ring oscillators. Each of the oscillators possesses its own set of eigenfrequencies that can be independently controlled by the external phase shifter. The coupling allows us to check on any common frequency that leads to the phase lock-in and power increase in the circuit. One of the ring oscillators includes a spin wave magnetic delay line made of Y3Fe2(FeO4)3, while the second oscillator includes an ordinary coaxial cable as a delay line. There are 22 eigenfrequencies for the spin wave oscillator and 4 eigenfrequencies for the oscillator with coaxial cable in the frequency band of operation. It takes less than 10 μs for the system to find the common frequency (if any). The most appealing property of the proposed circuit is that the processing time does not scale with the number of eigenfrequencies. Potentially, circuits with coupled active ring oscillators can be utilized to solve a variety of computational problems.