Algorithmic Complexity Theory for Quantum Simulation

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum simulation, a cornerstone of quantum computing, presents significant challenges in algorithm design and optimization. Traditional simulation methods often struggle with the inherent complexity of quantum systems, demanding substantial computational resources. This paper proposes a novel approach to algorithmic complexity theory specifically tailored for quantum simulation, focusing on the optimization of quantum state and interaction representation. We introduce a new, adaptive complexity measure designed to efficiently represent quantum states and interactions, thereby reducing the computational burden and enabling more practical simulations. The core mechanism centers around dynamically adjusting the complexity measure based on the system's specific characteristics, leading to improved performance across a range of quantum algorithms. We analyze the impact of this new measure through theoretical proofs and preliminary simulations, demonstrating its potential to significantly enhance the efficiency of quantum simulation.

DOI: 10.5281/zenodo.22199553

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