This paper proposes and implements a scheme to verify a prime periodicity model using the Quantum Phase Estimation (QPE) algorithm. Taking the prime p = 31 as an example, we construct a single-qubit unitary operator U = Rz(2π/p) whose eigenstate |1⟩ carries the phase φ = 1/31. QPE simulations are performed on the PyQPanda quantum simulator with counting qubit numbers t = 8, 10, 12, 14, 16, 18, 20, 22. Results show that the estimated phase gradually converges to the theoretical value as t increases, and the absolute error is only 3.3e-8 when t = 22, thereby validating the prime periodicity model. This work demonstrates the potential of quantum computation in verifying number-theoretic models and provides a repro- ducible quantum circuit example for studying prime periodicity.
Huang Feiyue (Mon,) studied this question.