Riemannian Quantum Circuit

TL;DR

This paper introduces a quantum circuit model linked to the zeros of the Riemann-zeta function, aiming to facilitate solving number theory problems via quantum algorithms.

Contribution

It presents the theoretical foundation of a quantum circuit associated with specific zeros of the Riemann-zeta function, bridging number theory and quantum computing.

Findings

Theoretical framework for a Riemann-zeta related quantum circuit

Potential for quantum algorithms to address number theory problems

Foundation for future experimental realization

Abstract

Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we present the theory of a quantum circuit related to a finite number of zeros of the Riemann-zeta function. The existence of such circuit will permit in the future the solution of some number theory problems through the realization of quantum algorithms based on those zeros.