Quantum Computation via Emergent Geometric Structures

Erik Sjöqvist, Vahid Azimi Mousolou, Carlo M. Canali

Mateus Rodrigues de Maria

This preprint develops the theoretical foundations of Emergent Quantum Geometry within the renormalizational framework of AGD (Análise Geométrica Dimensional). We introduce a geometric operator acting on quantum computational structures, formalize its renormalizational properties, and propose a structural bridge between emergent density geometry and modular architectures for quantum computation. The article establishes the conceptual and mathematical backbone for future developments in AGD-Quantum Computing, including stability analysis, renormalized flows, and possible hardware interpretations.

Jincheng Zhang

The study of geometric tensors and their topological properties has emerged as a significant area within advanced mathematics and physics, offering potential for novel computational paradigms. This paper investigates the application of topological structure-based methods to geometric tensors, aiming to design a quantum computing acceleration paradigm. Specifically, we explore a novel approach to represent and manipulate geometric tensors through a topological structure, and propose a new quantum algorithm predicated on this structure. The core mechanism centers on introducing a topological structure onto the tensor, allowing for efficient optimization and simulation. The potential for quantum acceleration stems from exploiting the inherent properties of topological spaces and the ability of quantum algorithms to explore complex geometric spaces. This research contributes to the development of more efficient and robust computational methods, and highlights the synergistic relationship between topological structures and quantum computation. Furthermore, we analyze the implications of this approach for various geometric manipulation tasks, including optimization problems and simulation of complex physical systems. The proposed quantum algorithm utilizes the topological structure to guide the computation, achieving significant speedups compared to classical methods. The work offers a novel perspective on utilizing topological structures to enhance quantum computing, with implications for diverse mathematical and physical applications. Ultimately, this paper presents a framework for constructing quantum algorithms that benefit significantly from the unique properties of geometric tensors, demonstrating the potential for quantum computation to surpass classical approaches in certain complex scenarios. This investigation focuses on the core mechanism of representing geometric tensors using topological structures, and explores how this structure can be leveraged to accelerate computations.

Eduardo Jose Bayro-Corrochano

Jincheng Zhang

This paper explores the intersection of geometric topology and quantum computation, focusing on the dynamic properties of quantum computation intrinsically linked through self-linking geometry. We introduce the concept of "self-linking geometric topology" to frame quantum algorithms as evolving geometric structures, and investigate how this approach validates quantum computations through self-similarity and topological properties. The core mechanism involves utilizing self-linking geometry to characterize the evolution of quantum states and identify critical points within the quantum algorithm. This research offers a novel validation method for quantum algorithms, potentially leading to improved algorithm design and robustness.

Shi-Liang Zhu, Paolo Zanardi A