HDQMF: Holographic Feature Decomposition Using Quantum Algorithms

This paper addresses the decomposition of holographic feature vectors in Hyperdimensional Computing (HDC) aka Vector Symbolic Architectures (VSA). HDC uses high-dimensional vectors with brain-like properties to represent symbolic information, and leverages efficient operators to construct and manipulate complexly structured data in a cognitive fashion. Existing models face challenges in decomposing these structures, a process crucial for understanding and interpreting a composite hypervector. We address this challenge by proposing the HDC Memorized-Factorization Problem that captures the common patterns of construction in HDC models. To solve this problem efficiently, we introduce HDQMF, a HyperDimensional Quantum Memorized-Factorization algorithm. HDQMF is unique in its approach, utilizing quantum computing to offer efficient solutions. It modifies crucial steps in Grover's algorithm to achieve hypervector decomposition, achieving quadratic speed-up.