Computational Complexity Analysis of Quantum Algorithms using Category Theory

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Traditional methods for analyzing the computational complexity of algorithms, predominantly rooted in classical computer models, struggle to accurately characterize the potential advantages offered by quantum computation. This work proposes a novel approach utilizing category theory to provide a more fundamental and abstract framework for assessing the complexity of quantum algorithms. Instead of focusing on the specifics of quantum hardware, we examine the underlying categorical structures that define the computational processes inherent in these algorithms. This allows us to identify and analyze complexity properties that are independent of the physical implementation. We define key concepts like quantum states as objects and quantum gates as morphisms, establishing a formal connection between quantum computation and category theory. This framework facilitates a more rigorous and generalized understanding of quantum complexity, potentially revealing new insights and providing a basis for comparing different quantum algorithms. The core claim is that traditional complexity analysis is inadequate, and the mechanism is the application of category theory for a more abstract and generalized framework.

DOI: 10.5281/zenodo.22636571

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