  This paper presents a quantum algorithm for efficiently decoding
hypervectors, a crucial process in extracting atomic elements from hypervectors
- an essential task in Hyperdimensional Computing (HDC) models for
interpretable learning and information retrieval. HDC employs high-dimensional
vectors and efficient operators to encode and manipulate information,
representing complex objects from atomic concepts. When one attempts to decode
a hypervector that is the product (binding) of multiple hypervectors, the
factorization becomes prohibitively costly with classical optimization-based
methods and specialized recurrent networks, an inherent consequence of the
binding operation. We propose HDQF, an innovative quantum computing approach,
to address this challenge. By exploiting parallels between HDC and quantum
computing and capitalizing on quantum algorithms' speedup capabilities, HDQF
encodes potential factors as a quantum superposition using qubit states and
bipolar vector representation. This yields a quadratic speedup over classical
search methods and effectively mitigates Hypervector Factorization capacity
issues.
