Appears in collection : 2024 - T1 - WS1 - Quantum simulators

I plan to start the seminar by presenting a discussion of the experimental realization with holographic techniques of the prime number quantum potential, defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. We also implemented the potential having as eigenvalues the first lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Further possible implementations are also considered. In the final part I will discuss how to possibly apply these potentials to factorization algorithms.