Neutrosophic Modelling of Qubit Uncertainty in Noisy Quantum Computing Systems

Abstract

Quantum computing exploits superposition and entanglement to perform computations beyond the capabilities of classical machines. However, practical quantum systems operate under substantial environmental noise, measurement uncertainty, and decoherence, leading to ambiguous or partially determined quantum states. Conventional probabilistic descriptions capture stochastic behaviour but do not explicitly represent indeterminacy arising from incomplete information or measurement ambiguity. In this work, we introduce a neutrosophic representation of qubit states that integrates principles of Neutrosophic Logic with the mathematical framework of Quantum Computing. In the proposed model, a qubit is characterised by three independent parameters representing truth, indeterminacy, and falsity. This formulation enables explicit representation of ambiguous quantum states and uncertain measurement outcomes. We extend the neutrosophic formalism to quantum gate operations and analyse how the model captures uncertainty propagation in quantum circuits. Through theoretical examples and graphical analysis, we demonstrate that neutrosophic representation provides a richer description of uncertainty compared with conventional probabilistic approaches. The proposed framework offers a conceptual pathway for improved modelling of noisy intermediate-scale quantum devices and may contribute to the development of uncertainty-aware quantum computing architectures.