QeHDC: Hyperdimensional Computing based on Quantum-enhanced binding and SuperClass Construction

Traditional Hyperdimensional Computing (HDC) offers a robust, brain-inspired framework for classification, but it faces significant storage and computational bottlenecks as data complexity increases. This paper explores whether quantum mechanical properties—specifically superposition, entanglement, and density matrix representations—can overcome these limitations to create a more efficient and scalable classification paradigm.

The authors propose QeHDC, a framework consisting of four main stages:

1. Hybrid Encoding: A two-step process that maps classical data into quantum amplitude states using random projection and sinusoidal transformations, effectively compressing data into a lower-dimensional qubit space.
2. Quantum Binding: An innovative operation that uses a predefined reference quantum state and specialized quantum circuits (CRX and CX gates) to associate data features without the exponential qubit growth typically associated with classical HDC binding.
3. Superclass Construction: Instead of simple averaging, the authors construct a density matrix for each class and use eigenvalue decomposition to extract the most representative 'SuperClass' template state.
4. One-Pass Training: The model learns class representations in a single pass through the data, eliminating the need for iterative backpropagation and making it highly suitable for resource-constrained environments.

Experimental evaluations using the Qiskit Aer Simulator and physical IBM quantum processors demonstrate that QeHDC achieves superior classification performance compared to traditional HDC and existing quantum-enhanced methods. The framework exhibits high robustness to noise and demonstrates cross-platform adaptability, successfully validating the algorithm on both ideal simulators and noisy physical hardware. The results suggest that quantum-inspired computational paradigms can significantly enhance the efficiency and expressiveness of high-dimensional computing for real-world machine learning tasks.