An experimental procedure to measure Floquet dynamics within a trapped-ion systems. Credit: HE Ran et al.The 1859 Riemann hypothesis is one of six Millennium unsolved problems. Its proof greatly aids in understanding the distribution laws for prime numbers. There has been a steady academic interest in the non-trivial zeros within the Riemann zeta functions for a while. This allows physicists reproduce prime numbers, and incites them to discover the essence Riemann hypothesis using a practical quantum approach.Prof. GUO Guangcan's research group from the University of Science and Technology of China, Chinese Academy of Sciences, used a trapped ion method to measure the locations of the Riemann Zeros.Together with Prof. Charles Creffield of Spain and Prof. German Sierra from Spain, the team measured experimentally the first 80 Riemann Zeros using a trapped-ion quibit in a Paul trap that is periodically driven by microwave fields. On July 14, the results were published in NPJ Quantum Information.The HilbertPlya conjecture, which combines the Riemann zeta functions with quantum theory, is the best of all possible solutions. This conjecture assumes that there is a quantum system where the eigenvalues for the Hamiltonian quantities match the Riemann zeros. This conjecture attracts many researchers who discover potential static Hamiltonians. These static Hamiltonians can be difficult to measure experimentally.The researchers did not prove the Riemann hypothesis. Instead, they created a physical embodiment of mathematical objects using advanced quantum technology. The trapped ion system was subjected at different times to a driving field. The resulting behavior was described by Floquet theory. They were able to observe the qubit's dynamics freeze as the driving parameters varied when an effect called "coherent destruction in tunneling" was discovered.The researchers were able to achieve 30 driving periods using high-fidelity quantum operations with a long coherence period and measure the first 80 Riemann Zeros. This is nearly twice the amount of previous work.This research provides a solid experimental base for researchers to study HilbertPlya and gain a better understanding of the relationship between quantum systems and the Riemann hypothesis.More information: Ran He et al, Riemann zeros from Floquet engineering a trapped-ion qubit, npj Quantum Information (2021). Ran He et al, Riemann zeros from Floquet engineering a trapped-ion qubit,(2021). DOI: 10.1038/s41534-021-00446-7
