Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

TL;DR

This paper explores the Riemann Hypothesis through quantum physics and information theory, using four different approaches to provide evidence supporting its validity.

Contribution

It introduces four novel perspectives combining quantum states, Hilbert-Polya conjecture, randomness, and number theory to analyze the Riemann Hypothesis.

Findings

RH avoids indeterminacy in coherent states

Quantum circuit approach supports RH

Number theory methods reinforce RH validity

Abstract

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 in the inner product of two coherent states. In the second case, the Hilber-Polya conjecture with a quantum circuit is considered. In the third case, randomness, entanglement and the Moebius function are used to discuss the RH. At last, in the fourth case, the RH is discussed by inverting the first derivative of the Chebyshev function. The results obtained reinforce the belief that the RH is true.