The Riemann Hypothesis – Quantum Branching

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper investigates the Riemann Hypothesis through the lens of quantum entanglement, proposing a novel theoretical model that posits the emergence of 'quantum branches' within the zeta function distribution. We explore a quantum-mechanical framework to simulate the evolution of the zeta function, incorporating entanglement as a fundamental process driving the formation of these branches. The goal is to provide a potential pathway for understanding the hypothesis and its connection to the nascent field of quantum computation. This work aims to initiate a discussion about the potential for a fundamentally new approach to the Riemann Hypothesis.

DOI: 10.5281/zenodo.22496148

Related papers

Title: Quantum-Enhanced Riemann Hypothesis via Entangled Variables

Jincheng Zhang

The Riemann Hypothesis, a long-standing and stubbornly unsolved problem in number theory, has captivated mathematicians for over 150 years. Current computational methods struggle to definitively prove or disprove it, highlighting a significant gap in our understanding of the zeta function. This paper proposes a novel approach to tackle this problem utilizing quantum-enhanced measurement techniques and entangled variables. We outline a new algorithm for exploring the Riemann Hypothesis, leveraging the correlations between entangled particles to identify subtle patterns within the zeta function. The core mechanism centers on creating entangled particles to probe the structure of the zeta function, potentially revealing previously missed connections. This investigation leverages a hybrid quantum-classical approach, combining the precision of quantum mechanics with the analytical power of classical computation. The goal is to develop a framework that can potentially lead to new insights into the Riemann Hypothesis and provide a more robust theoretical foundation.

Aug 29, 20260 citations

Title: Quantum-Enhanced Riemann Hypothesis

Jincheng Zhang

The Riemann Hypothesis, a long-standing unsolved problem in mathematics, concerns the distribution of prime numbers. Despite extensive research, no definitive proof remains elusive. This paper explores a novel quantum algorithm designed to approximate the Riemann zeta function, aiming to provide exponential speedups over classical methods. We propose a hybrid quantum-classical approach, utilizing quantum superposition and entanglement to efficiently explore the zeta function's complex landscape, ultimately leading to a significant computational advantage. This research focuses on the fundamental potential of quantum computation to address this mathematical challenge.

Sep 1, 20260 citations

Quantum Hidden Variables and Riemann Hypothesis

Doju K. Degefa

In this paper, I explore the intriguing connection between hidden variables in quantum mechanics and the nontrivial zeros of the Riemann zeta function.Despite the apparent randomness in quantum phenomena, I demonstrate that deterministic hidden variables can coexist without violating Bell's inequalities, particularly in scenarios involving small angles.Using MATLAB simulations and a simplified space-time model, I illustrate this relationship, shedding light on the fundamental nature of quantum systems.This research not only deepens our understanding of quantum mechanics but also opens new avenues for investigating the Riemann zeta function's implications, potentially transforming our approach to both fields.

Multimedia ResearchJan 1, 20240 citations

The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions

ShiJie Wei, Yue Zhai, Quanfeng Lu +7 more

The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Establishing connections between the RH and physical phenomena could offer new perspectives on its physical origin and verification. Here, we establish a direct correspondence between the nontrivial zeros of the zeta function and dynamical quantum phase transitions (DQPTs) in two realizable quantum systems, characterized by the averaged accumulated phase factor and the Loschmidt amplitude, respectively. This precise correspondence reveals that the RH can be viewed as the emergence of DQPTs at a specific temperature. We experimentally demonstrate this correspondence on a five-qubit spin-based system and further propose an universal quantum simulation framework for efficiently realizing both systems with polynomial resources, offering a quantum advantage for numerical verification of the RH. These findings uncover an intrinsic link between nonequilibrium critical dynamics and the RH, positioning quantum computing as a powerful platform for exploring one of mathematics' most enduring conjectures and beyond.

quant-pharXiv:2511.11199Nov 17, 2025

Title: Higher-Order Riemann Hypothesis – Quantum Correlation as a Constraint

Jincheng Zhang

The Riemann Hypothesis, a long-standing unsolved problem in number theory, poses a fundamental challenge to our understanding of the distribution of prime numbers. While its impact on the arithmetic of prime numbers is well-established, its subtle implications for the underlying structure of quantum mechanics remain largely unexplored. This paper investigates the potential for quantum correlations within the prime number distribution to provide a novel constraint on the fundamental laws of quantum mechanics, proposing a new mathematical tool to quantify these correlations and demonstrate their significance. We argue that these correlations, if quantifiable, could reveal a deeper connection between number theory and quantum phenomena, potentially leading to new insights into the nature of reality. This work will explore the potential for entanglement-based approaches to quantify these correlations, providing a rigorous theoretical framework for investigating this intriguing connection.

Aug 31, 20260 citations

Title: The Riemann Hypothesis Revisited: Quantum-Enhanced Non-Euclidean Geometry – A New Computational Paradigm

Jincheng Zhang

The Riemann Hypothesis, a cornerstone of number theory, remains one of the most persistent and challenging unsolved problems in mathematics. Its implications extend far beyond its immediate mathematical value, touching upon fundamental questions about the nature of space and the distribution of prime numbers. This paper explores a novel computational paradigm centered on quantum entanglement, proposing a method for exploring the Riemann Hypothesis space through a quantum superposition of geometries. We investigate the potential of this approach to identify subtle patterns and correlations that are currently obscured by classical computation, potentially offering a pathway to a deeper understanding of the hypothesis's implications. We outline a preliminary algorithm and discuss the theoretical implications of utilizing quantum entanglement to address this longstanding challenge.

Sep 7, 20260 citations