Accurately Measured Riemann Zero Locations

Experimental procedure to measure Floquet dynamics in a trapped ion system. Credit: HE Ran et al.

Raised in 1859, the Riemann Hypothesis is one of the six unsolved Millennium Problems, and its proof greatly facilitates our understanding of the laws of prime number distribution. For a long time there has been growing academic interest in the non-trivial zeros of the Riemann-his zeta function. This will enable physicists to reproduce prime numbers and will inspire them to use viable quantum approaches to discover the essence of the Riemann hypothesis.

To precisely measure the location of the Riemann zero, the research team of Professor GUO Guangcan of the University of Science and Technology of China (USTC), Chinese Academy of Sciences, employed a trapped ion system.

The team, along with Spanish theoretical physicists Professor Charles Creffield and German Sierra, used trapped ion qubits in a pole trap periodically driven by a microwave field to find the first 80 Riemann zeros. measured experimentally. The results were published in NPJ Quantum Information on July 14.

Among all possible solutions, the Hilbert-Polya conjecture combines Riemann’s zeta function and quantum theory. This conjecture assumes the existence of a quantum system whose eigenvalues ​​of the Hamiltonian quantity agree with the Riemann zero. Researchers were fascinated by this conjecture and found many potential static Hamiltonians. However, it is difficult to measure these static Hamiltonians experimentally.

In this study, researchers chose not to prove the Riemann hypothesis, but to use advanced quantum techniques to provide physical realizations of mathematical objects. In trapped ion systems, ions are exposed to a periodic driving field and consequently their behavior was described by Floquet theory. When an effect called “coherent breaking of tunneling” appeared, we could observe the qubit dynamics freezing when the driving parameters were varied.

Thanks to high-fidelity quantum manipulation and long coherence times, the researchers achieved 30 driving periods and measured the first 80 Riemann zeros. This is an improvement of his nearly two orders of magnitude over previous studies.

This work provides an important experimental basis for researchers to study the Hilbert-Polya conjecture and to better understand the relationship between the Riemann hypothesis and quantum systems.

New Insights to Prove Math’s Million Dollar Problem: The Riemann Hypothesis (Updated)

For more information:
Ran He et al., Floquet’s Riemann zeros designed trapped ion qubits, npj quantum information (2021). DOI: 10.1038/s41534-021-00446-7

Provided by the Chinese Academy of Sciences

Quote: Accurately measured Riemann zero position (11 Aug 2021) retrieved on 11 Sep 2022 from

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