Identifying the Riemann zeros by periodically driving a quantum simulator. (arXiv:1903.07819v2 [quant-ph] UPDATED)

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 function and the first two zeros of P\'olya's 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. In this manner, our study provides a new insight into the
P\'olya--Hilbert conjecture for quantum systems.

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