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Quantum Complexity Theory - Computational Landscape Analysis

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

Quantum Complexity Theory (QCT) represents a paradigm shift in our understanding of computational complexity, moving beyond classical approaches to explore the potential of quantum mechanics. This paper proposes a novel algorithm, the "Entangled Search Algorithm" (ESA), designed to analyze the computational landscape of a given problem, leveraging quantum entanglement to efficiently identify optimal solutions. We argue that this approach offers a significant advantage over existing methods, particularly in tackling complex problems with inherent quantum features. The ESA utilizes quantum entanglement to create a dynamic landscape of possibilities, enabling a more targeted and potentially faster search for solutions. This work details the fundamental concepts, algorithm implementation, and preliminary results demonstrating the potential of this approach.

DOI
10.5281/zenodo.22280720

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Quantum Complexity Theory (QCT) represents a paradigm shift in our understanding of computational complexity, moving beyond classical approaches to explore the potential of quantum mechanics. This paper proposes a novel algorithm, the "Entangled Search Algorithm" (ESA), designed to analyze the computational landscape of a given problem, leveraging quantum entanglement to efficiently identify optimal solutions. We argue that this approach offers a significant advantage over existing methods, particularly in tackling complex problems with inherent quantum features. The ESA utilizes quantum entanglement to create a dynamic landscape of possibilities, enabling a more targeted and potentially faster search for solutions. This work details the fundamental concepts, algorithm implementation, and preliminary results demonstrating the potential of this approach.
Quantum Complexity Theory (QCT) offers a novel framework for algorithm design, predicated on the principle that certain computational problems exhibit inherent quantum complexity. This paper explores the application of QCT to identify problems with a significantly enhanced computational advantage when tackled using quantum algorithms. We argue that by leveraging the unique properties of quantum mechanics, we can potentially develop algorithms that outperform their classical counterparts in solving complex problems, demonstrating a paradigm shift in algorithmic design. This work lays the foundation for a new area of research with significant implications for the future of computational science and engineering.
This paper explores the potential of quantum entanglement as a computational tool to tackle specific mathematical problems, drawing inspiration from the Riemann-Hilbert Conjecture. We propose a novel quantum algorithm designed to exploit entanglement to achieve a practical, verifiable advantage over classical methods for certain complex calculations. The paper outlines the core mechanism, details the algorithm's implementation, and discusses preliminary results demonstrating the feasibility of leveraging entanglement for computation. We argue that this approach represents a significant step toward understanding and utilizing quantum phenomena for computational purposes, potentially offering a new avenue for tackling problems within the realm of mathematical complexity.
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