Quantum Coherence-Based Computational Complexity Analysis

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper presents a novel approach to analyzing the computational complexity of quantum algorithms by leveraging the concept of quantum coherence. Traditional methods for assessing quantum complexity often rely on circuit depth, qubit count, or gate complexity, which can be insufficient in capturing the nuances of quantum computation. We introduce a framework that explicitly incorporates the calculation of quantum coherence, recognizing it as a fundamental resource in quantum computation. The core idea is that the precision and duration of quantum coherence directly correlate with the computational effort required. We define a mathematical model that quantifies coherence decay and its impact on algorithm execution time. This model allows us to derive tighter bounds on the complexity of quantum algorithms, particularly those that rely heavily on sustained coherence. Furthermore, we explore the implications of coherence limitations on the feasibility of certain quantum algorithms and suggest potential strategies for mitigating these effects. This work contributes a new perspective on quantum complexity analysis, providing a more accurate and potentially more scalable method for evaluating quantum algorithms.

DOI: 10.5281/zenodo.22273857

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