Riemann zeros from Floquet engineering a trapped-ion qubit

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The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in random matrix theory and quantum chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped-ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.
© The Author(s) 2021 C.E.C. was supported by the Spanish MINECO through grant FIS2017-84368-P, and G.S. by PGC2018-095862-B-C21, QUITEMAD+ S2013/ICE-2801, SEV-2016-0597 and the CSIC Research Platform on Quantum Technologies PTI-001. R.H., M.Z.A., J.M.C., Y.F.H., Y.J.H., C.F.L., and G.C.G. were supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304100 and 2016YFA0302700), the National Natural Science Foundation of China (Grant Nos. 11874343, 61327901, 11774335, and 11734015), Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSW-SLH003), the Fundamental Research Funds for the Central Universities (Grant Nos. WK2470000026, WK2470000027, and WK2470000028), and Anhui Initiative in Quantum Information Technologies (Grant Nos. AHY020100 and AHY070000).