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Quantum State Real Complexity (QSRC)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

This paper introduces the concept of Quantum State Real Complexity (QSRC), proposing that the complexity associated with a quantum state is fundamentally distinct from computational complexity. Instead of focusing on the steps required for a calculation, QSRC posits that quantum states inherently possess a physical complexity, denoted as [Cψ], which reflects the underlying structure and relationships within the quantum system. This framework shifts the paradigm in understanding quantum systems, potentially leading to novel insights and discoveries. The core argument centers around the limitations of traditional computational models in fully capturing the essence of quantum behavior, particularly regarding entanglement and superposition. The investigation utilizes quantum simulation as a primary method for exploring and characterizing this physical complexity. The potential implications of QSRC are significant, suggesting a pathway toward a deeper understanding of quantum mechanics and potentially unlocking new quantum properties.

DOI
10.5281/zenodo.21974817

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This paper introduces the concept of Quantum State Real Complexity (QSRC), proposing that the complexity associated with a quantum state is fundamentally distinct from computational complexity. Instead of focusing on the steps required for a calculation, QSRC posits that quantum states inherently possess a physical complexity, denoted as [Cψ], which reflects the underlying structure and relationships within the quantum system. This framework shifts the paradigm in understanding quantum systems, potentially leading to novel insights and discoveries. The core argument centers around the limitations of traditional computational models in fully capturing the essence of quantum behavior, particularly regarding entanglement and superposition. The investigation utilizes quantum simulation as a primary method for exploring and characterizing this physical complexity. The potential implications of QSRC are significant, suggesting a pathway toward a deeper understanding of quantum mechanics and potentially unlocking new quantum properties.
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.
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