Title: Quantum-Enhanced Riemann Hypothesis

Jincheng Zhang

Published Sep 1, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.22220274

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: 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

Quantum-Enhanced Riemann Hypothesis Testing

Jincheng Zhang

The Riemann Hypothesis, a long-standing unsolved problem in number theory, remains one of the most challenging mathematical puzzles. Traditional methods struggle to efficiently explore the vast solution space, hindering progress towards a definitive proof. This paper proposes a novel approach utilizing quantum-enhanced Riemann Hypothesis testing, specifically employing a hybrid quantum-classical algorithm. We hypothesize that quantum superposition, coupled with probabilistic error correction, can dramatically accelerate the search for solutions and provide novel insights into the hypothesis. The core mechanism involves a 'Quantum Monte Carlo' simulation, refined with classical optimization, designed to effectively navigate the hypothesis space. This work offers a potential paradigm shift in the testing process, potentially unlocking new avenues for investigation and pushing the boundaries of number-theoretic research.

Aug 31, 20260 citations

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: Non-Locality-Based Quantum Algorithm for Superposition

Jincheng Zhang

Quantum computing stands on the cusp of a revolution, offering the potential to solve problems intractable for classical computers. A key enabler of this revolution is the ability to harness quantum entanglement – a phenomenon where two or more quantum particles become inextricably linked, regardless of the distance separating them. This paper introduces a novel quantum algorithm predicated on entanglement, aiming to create a non-local computational framework that transcends the limitations of traditional quantum architectures. We propose a quantum algorithm centered around leveraging instantaneous correlations to enable parallel computation across vast distances, fundamentally altering our approach to problem-solving. The core mechanism of this algorithm involves meticulously crafted entanglement protocols that exploit correlations to achieve exponential speedups in specific computational tasks. This work presents a fundamentally new perspective on quantum computation, focusing on the potential of non-locality to unlock unprecedented computational capabilities. The algorithm's design incorporates key mathematical concepts and proofs necessary for establishing its validity. The resultant algorithm demonstrates, through simulations and preliminary analysis, the potential for significant performance improvements compared to existing quantum algorithms. This paper also discusses the challenges and future research directions associated with this groundbreaking approach.

Aug 31, 20260 citations

Title: Dynamically Generated Prime Number Sequences via Quantum Simulation

Jincheng Zhang

The quest for prime numbers remains a fundamental challenge in mathematics, driving a persistent desire for more efficient prime number generation techniques. Classical methods often struggle to produce sufficient numbers, while the search for novel prime distribution patterns is a long-standing endeavor. This paper explores a novel approach utilizing quantum simulation to generate and analyze prime number sequences with significantly enhanced density. We propose a quantum simulation technique that leverages quantum entanglement to create a highly complex, multi-scale model of prime number distribution. This model allows for the identification of intricate patterns and distributions, far exceeding the capabilities of classical computation. We detail the theoretical framework, the quantum algorithm implementation, and preliminary results demonstrating a substantial increase in prime number density compared to existing methods. This advancement holds the potential to revolutionize prime number discovery and contribute to a deeper understanding of the fundamental properties of prime numbers.

Sep 7, 20260 citations