Identifying the Riemann zeros by periodically driving a single qubit
arXiv:1903.07819 · doi:10.1103/PhysRevA.101.043402
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 solve 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 have been experimentally feasible.Here, we report the first experiment to identify the first non-trivial zeros of the Riemann zeta function and the first two zeros of Pólya's fake zeta function, using a novel Floquet method, through properly designed periodically driving functions. According to this method, the zeros of these functions are characterized by the occurrence of crossings of quasi-energies when the dynamics of the system are frozen. The experimentally obtained zeros are in excellent agreement with their exact values. Our study provides the first experimental realization of the Riemann zeros, which may provide new insights into this fundamental mathematical problem.
arXiv comment5 pages, 7 figures
References in corpus (22)
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Observation of a Discrete Time Crystal
- Dynamical control of matter-wave tunneling in periodic potentials
- Modeling spontaneous breaking of time-translation symmetry
- Single-qubit quantum memory exceeding -minute coherence time
- Floquet Fractional Chern Insulator in Doped Graphene
- Exploring dynamic localization with a Bose-Einstein condensate
- Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
- Physics of the Riemann Hypothesis
- Hamiltonian for the zeros of the Riemann zeta function
- Location of crossings in the Floquet spectrum of a driven two-level system
- Measuring a Dynamical Topological Order Parameter in Quantum Walks
- Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
- The H=xp model revisited and the Riemann zeros
- Nuclei, Primes and the Random Matrix Connection
- Quantum mechanical potentials related to the prime numbers and Riemann zeros
- Riemann zeta function and quantum chaos
- The Riemann zeros as spectrum and the Riemann hypothesis
- Finding zeros of the Riemann zeta function by periodic driving of cold atoms
- Quantum graphs whose spectra mimic the zeros of the Riemann zeta function
- Quantum simulation of the Riemann-Hurwitz zeta function