基于量子信息熵的算法复杂度分析

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper investigates the application of quantum information entropy as a novel approach to analyzing algorithm complexity. Traditional methods often rely on classical computational models and may not fully capture the resource demands inherent in quantum algorithms. We propose a framework where algorithms are translated into quantum information processing steps, and quantum information entropy is utilized to quantify the complexity of these processes. The core claim is that this approach offers a more accurate assessment of computational resource requirements, ultimately guiding the design and optimization of algorithms. We present a theoretical framework and explore potential applications, highlighting the unique insights gained through the lens of quantum information entropy. The analysis focuses on identifying key metrics related to entanglement, coherence, and quantum state manipulation, which directly influence the entropy values. We demonstrate how variations in these metrics can significantly impact the overall complexity of an algorithm. Furthermore, we discuss the limitations of this approach and suggest future research directions.

DOI: 10.5281/zenodo.22315755

Related papers

Quantum Computation Complexity Theory Based on Quantum Information Entropy

Jincheng Zhang

This paper explores the application of quantum information entropy to the theory of computational complexity. We posit that quantum information entropy can serve as a novel metric for quantifying the complexity of quantum algorithms and their associated resource requirements. The core argument is that traditional measures of computational complexity, such as circuit depth or quantum gate count, often fail to fully capture the inherent challenges posed by quantum systems. By leveraging entropy, we aim to provide a more nuanced and potentially more accurate assessment of the difficulty of quantum computations. This work introduces a framework for analyzing quantum algorithms through the lens of information entropy, exploring relationships between algorithmic complexity, entropy generation, and the resources needed to execute these algorithms. Specifically, we examine how entropy can be used to characterize the 'quantumness' of an algorithm and its impact on the overall computational cost. The ultimate goal is to develop a more robust and predictive model for quantum computation, leading to improved algorithm design and resource allocation. ---

Aug 31, 20260 citations

Computational Complexity Analysis of Quantum Algorithms using Information Theory

Jincheng Zhang

This paper explores the application of information theory to analyze the computational complexity of quantum algorithms. Traditional approaches to complexity analysis often rely on circuit models and gate complexity, which can be insufficient for fully characterizing the resource requirements of quantum computation. We propose utilizing information-theoretic concepts, specifically quantum entropy and mutual information, to provide a more nuanced understanding of how quantum circuits process information. This approach allows us to quantify the information-theoretic limits of quantum algorithms, providing insights into the number of qubits and gates necessary for efficient execution. We examine several key aspects, including the role of entanglement, the impact of measurement, and the relationship between quantum entropy and algorithmic complexity. The goal is to establish a framework for assessing quantum algorithms based on their fundamental information-processing capabilities, moving beyond purely circuit-based evaluations. This work contributes to a deeper theoretical understanding of quantum computation and its potential limitations.

Sep 2, 20260 citations

自适应信息论的量子纠缠分析

Jincheng Zhang

This research investigates the potential of self-adaptive information theory to analyze quantum entanglement, aiming to identify novel advantages in algorithm optimization and information processing. We propose a novel framework leveraging the unique properties of quantum entanglement to dynamically adjust and refine information-theoretic analysis, ultimately uncovering potential computational gains and strategic insights. The core mechanism involves utilizing entanglement as a 'channel' for information transfer, enabling enhanced algorithmic efficiency and a deeper understanding of quantum information's inherent capabilities. This study presents a preliminary investigation utilizing a simplified model to demonstrate the potential of this approach. The research focuses on exploring the impact of strategically manipulating entanglement parameters on the results of various information-theoretic metrics.

Aug 31, 20260 citations

基于自适应的量子信息熵的计算 - 量子信息熵的计算框架

Jincheng Zhang

This paper introduces a novel computational framework for quantifying quantum information entropy, leveraging the principles of quantum entanglement and quantum algorithms. The framework aims to provide efficient and accurate entropy calculations, addressing limitations of traditional approaches. We propose a quantum-enhanced entropy calculation method centered around the manipulation of quantum entanglement, incorporating optimization techniques to accelerate the calculation process. The core mechanism focuses on utilizing entangled qubits to explore the complex probability distribution underlying quantum information entropy. This offers a fundamentally different approach to entropy computation, capitalizing on the unique properties of quantum systems. The proposed framework demonstrates potential for improved accuracy and scalability compared to existing methods, offering a promising step towards practical quantum information processing.

Sep 6, 20260 citations

Title: Quantum Entanglement-Based Computational Complexity

Jincheng Zhang

Quantum entanglement, a peculiar phenomenon in quantum mechanics, offers a fundamentally different approach to computation than classical systems. This research explores the potential of leveraging entanglement as a core building block for computational complexity, proposing a novel method for quantifying the difficulty of algorithms through the development of an entanglement metric. The core claim is that certain computational tasks exhibit inherent complexity that cannot be adequately explained by classical complexity theory, and that this approach could lead to a deeper understanding of the limits of computation. The paper details the creation of an entanglement metric, a mathematical framework designed to directly relate entanglement properties to computational resource requirements, and demonstrates its ability to accurately estimate the complexity of specific algorithms. This work represents a significant step towards a more rigorous and predictive analysis of computational challenges, potentially uncovering previously unrecognized limitations within the realm of algorithmic complexity.

Sep 1, 20260 citations

量子纠缠信息熵建模与计算

Jincheng Zhang

Quantum entanglement offers a fundamentally different approach to information processing compared to classical systems, promising enhanced computational capabilities. This paper explores the application of quantum entanglement to modeling and quantifying information entropy, specifically targeting the complexities inherent in quantum systems. We propose a novel approach that leverages the unique properties of entangled states to achieve precise entropy calculations and translate them into computationally viable operations. The core mechanism centers around a quantum entanglement-based encoding scheme, which allows for a more accurate representation of quantum information entropy than traditional methods. This research aims to develop a robust and scalable framework for analyzing and manipulating quantum information, potentially unlocking new avenues for quantum computing and information science. The proposed method offers a significant advance in the field of quantum information theory and its practical implementation.

Sep 5, 20260 citations