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 solving 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 has been experimentally feasible. Here we report an experiment using a Floquet method to identify the first nontrivial zero of the Riemann. function and the first two zeros of Polya's function. Through properly designed periodically driving functions, the zeros of these functions are characterized by the occurrence of crossings of quasienergies when the dynamics of the system is frozen. The experimentally obtained zeros are in good agreement with their exact values. Our study provides the experimental realization of the Riemann zeros in a quantum system, which may provide insights into the connection between the Riemann function and quantum physics.