Prime Number Identification Demonstrated with Quantum Processors Using a New Rescaling-Based Noise Mitigation Technique

We implement a quantum protocol for prime number identification based on entanglement dynamics, using IBM quantum processors. The method links the primality of an integer to specific Fourier components extracted from the time evolution of entanglement in a bipartite quantum system. To mitigate experimental noise, we introduce a noise-mitigation method based on a global rescaling factor, which is calibrated on a subset of circuits and extrapolated across different configurations. Theoretical support is provided by a new analytical bound for the Fourier modes derived assuming an initial uniform superposition state. This new bound enhances the separation between prime and composite numbers under moderate experimental deviations. These results represent a step toward practical number-theoretic applications on noisy intermediate-scale quantum (NISQ) devices.