Publication: Identifying the Riemann zeros by periodically driving a single qubit
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2020-04-20
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Amercican Physical Society
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Abstract
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 solving 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 has been experimentally feasible. Here we report an experiment using a Floquet method to identify the first nontrivial zero of the Riemann. function and the first two zeros of Polya's function. Through properly designed periodically driving functions, the zeros of these functions are characterized by the occurrence of crossings of quasienergies when the dynamics of the system is frozen. The experimentally obtained zeros are in good agreement with their exact values. Our study provides the experimental realization of the Riemann zeros in a quantum system, which may provide insights into the connection between the Riemann function and quantum physics.
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©2020 Amercican Physical Society
This work was supported by the National Key Research and Development Program of China (Grants No. 2017YFA0304100 and No. 2016YFA0302700), the National Natural Science Foundation of China (Grants No.11874343, No. 61327901, No. 11774335, No. 11474270, No. 11734015, and No. 11821404), Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSW-SLH003), the Fundamental Research Funds for the Central Universities (Grants No. WK2470000026, No. WK2470000027, and No. WK2470000028), and Anhui Initiative in Quantum Information Technologies (Grants No. AHY020100 and No. AHY070000). G.S. was supported by Grants No. PGC2018-095862-B-C21, No. QUITEMAD+ S2013/ICE-2801, and No. SEV-2016-0597 (Spain) and the CSIC Platform on Quantum Technologies PTI-001. C.E.C. was supported by Spain's MINECO through Grant No. FIS2017-84368-P.