Quantum Fourier transform of the Prime state

Abstract

Quantum Computation is a growing and important field in applied physics research, so further theoretical foundations are continuously requested. In this regard, some mathematical algorithms have already been proposed. For instance, creating a quantum state representing the superposition of all prime number less than a value N has been shown to be efficient, and also applying the Quantum Fourier transform to it. This paper discusses the result of doing this operation and shows that some deep mathematical properties of prime numbers, such the Prime Counting function or biases in primes distribution, like the Chebyshev bias, are easily accessible via a systematic statistical approach