Core Claim: Leveraging adaptive topology in non-Euclidean spaces, we construct a quantum circuit with adaptive topology, capable of performing complex quantum logic operations.

Jincheng Zhang

Published Sep 2, 2026• 0 citations

Abstract

The study of quantum circuits presents a significant challenge in designing robust and flexible quantum algorithms. Traditional approaches often rely on static, pre-defined topologies, limiting the circuit's adaptability to varying quantum system states. This paper proposes a novel approach to quantum circuit design, utilizing adaptive topology within a non-Euclidean space. We introduce a dynamic topology framework that adjusts to the quantum system's state, enabling the circuit to evolve in response to changes in the system's properties. This adaptive approach, achieved through a carefully designed self-consistent set, allows for the creation of quantum circuits exhibiting complex and dynamic behavior. The core of our work focuses on establishing a mechanism for the circuit to continuously adapt its topology, ensuring the continued operation of the quantum algorithm. This leads to a new method for building quantum circuits with enhanced computational capabilities and greater resilience to noise. The resultant quantum circuits will demonstrate a greater degree of complexity and adaptability compared to static topology-based circuits, representing a significant advancement in the field. We present a mathematical model and a preliminary simulation demonstrating the efficacy of this approach.

DOI: 10.5281/zenodo.22245598

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