Quantum Computation Complexity Theory Based on Quantum Information Entropy

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

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. ---

DOI: 10.5281/zenodo.22193367

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