Quantum Search for HDC Decomposition Becomes Qubit-Efficient.

This research introduces a novel quantum framework designed to make Hyperdimensional Computing (HDC) decomposition more practical and qubit-efficient. HDC represents symbols using high-dimensional hypervectors, and their decomposition involves searching a vast space of candidate tuples, which is computationally intensive. Previous quantum approaches offered a quadratic search speedup but suffered from high qubit requirements, typically scaling with the hypervector dimension (O(D)). The new framework drastically reduces this cost to O(log D) by implementing logarithmic hypervector and binding encodings. Combined with a reversible hypervector lookup operator and a modified Dürr-Høyer search procedure, this method maintains the O(sqrt(N^F)) search complexity while achieving up to 2,000 times fewer qubits. This breakthrough makes quantum HDC decomposition feasible for larger-scale problems, opening new avenues for quantum machine learning applications.