Intelligent Computing

Orthogonality in Quantum-Probabilistic Machine Learning: An Investigation on Multiqubit Encoding

Sheng-Chen Bai, Kun Zhang, Shi-Ju Ran

Published Jan 1, 2026• 0 citations

Abstract

The “black-box” nature of deep learning models fundamentally limits their reliability in critical applications. Tensor networks (TNs), drawing on their interpretable, quantum-probabilistic foundations, offer a promising pathway toward more transparent machine learning (ML). However, a systematic understanding of their capabilities and limitations remains an open challenge. Here, we establish a fundamental connection between a core property of quantum systems, namely, the catastrophe of orthogonality (COO), and the representational power and generalization performance of quantum-probabilistic TN models. Taking the Fashion Modified National Institute of Standards and Technology dataset, we propose 2 multiqubit data encoding schemes and demonstrate that key hyperparameters, such as the number of qubits, feature count, and mapping angle, modulate the onset of COO. This control mechanism directly dictates the model’s capacity, revealing that over-fitting can be interpreted as a specific regime of the quantum state space. Our work provides a theoretical lens, grounded in quantum many-body physics, for interpreting ML models. It positions TNs not merely as efficient computational tools but as a foundational framework for building inherently interpretable and reliable ML models.

DOI: 10.34133/icomputing.0232

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