Identifying the Riemann zeros by periodically driving a single qubit

Abstract: The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solve this hypothesis is to connect the problem with the spectrum of the physical Hamiltonian of a quantum system. However, none of the proposed quantum Hamiltonians have been experimentally feasible.Here, we report the first experiment to identify the first non-trivial zeros of the Riemann zeta function and the first two zeros of P\'olya's fake zeta function, using a novel Floquet method, through properly designed periodically driving functions. According to this method, the zeros of these functions are characterized by the occurrence of crossings of quasi-energies when the dynamics of the system are frozen. The experimentally obtained zeros are in excellent agreement with their exact values. Our study provides the first experimental realization of the Riemann zeros, which may provide new insights into this fundamental mathematical problem.