Title: Non-Euclidean Quantum State Space Description

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Quantum state space description is a fundamental concept in quantum mechanics, but its application to practical algorithms is limited by the inherent geometric constraints of the Hilbert space. This paper explores a novel approach to quantum state space representation, leveraging non-Euclidean geometry to provide a geometrically-aligned framework for quantum algorithms. We propose a method for constructing quantum states and performing computations that directly reflects the properties of a non-Euclidean space, potentially unlocking new algorithmic possibilities. The core mechanism centers around establishing a mapping between quantum states and geometric primitives, allowing for the creation of algorithms that are inherently more robust and adaptable to non-Euclidean geometries. This work introduces a new methodology for quantum state representation and computation, aiming to overcome the limitations of traditional geometric approaches and facilitate the development of fundamentally new quantum algorithms.

DOI: 10.5281/zenodo.22497433

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