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Title:
Quantum simulation of the Riemann zeta function using a driven ion
Speaker:
Abstract:
The non-trivial zeros of the Riemann zeta function are central objects in number theory, and have also attracted the attention of physicists working in random matrix theory and quantum chaos for many years. In this talk I will show how a quantum simulation technique termed "Floquet engineering" can be used to modify the spectrum of a periodically-driven system, so that its quasienergies correspond to the imaginary components of the Riemann zeros. I will go on to show how this has been implemented for a trapped ion qubit held in a Paul trap, allowing the position of the zeros to be determined by measuring the tunneling dynamics of the qubit. By scanning over the amplitude of the driving field, the locations of the Riemann zeros can be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm. References: 1. "Riemann zeros from Floquet engineering a trapped-ion qubit", Ran He, et al., npj Quantum Inf 7, 109 (2021). 2. "Identifying the Riemann zeros by periodically driving a single qubit", Ran He, et al., Phys. Rev. A 101, 043402 (2020).
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