Hyperdimensional Quantum Factorization

This paper presents a quantum algorithm for efficiently from components of the data are encoded into high-dimensional vectors decoding hypervectors, a crucial process in extracting atomic elements with brain-inspired properties [9, 13, 20, 19, 8]. The HDC operators from hypervectors--an essential task in Hyperdimensional - binding, bundling, and permutation - construct sets, associations, Computing (HDC) models for interpretable learning and information and sequences respectively, facilitating the interpretable creation retrieval. HDC employs high-dimensional vectors and efficient operators and manipulation of complex objects for data representation, to encode and manipulate information, representing complex learning, and processing. For learning, an HDC model makes decisions objects from atomic concepts. When one attempts to decode a hypervector by evaluating the similarity between query and model hypervectors that is the product (binding) of multiple hypervectors, the factorization [11, 26, 12, 18, 16]; for cognitive processing, an HDC model becomes prohibitively costly with classical optimizationbased retrieves information directly over the hyperspace with HDC operators; methods and specialized recurrent networks, an inherent consequence it then decodes the information with similarity functions and of the binding operation. We propose HDQF, an innovative the atomic hypervectors [9, 22, 30]. Recent work has shown great quantum computing approach, to address this challenge. By exploiting advantages of HDC in enhancing the cognitive capability of neural parallels between HDC and quantum computing and capitalizing networks in an explainable fashion [7]: a neural network learns to on quantum algorithms' speedup capabilities, HDQF encodes potential encode and perform HDC-like composition of the data over Raven's factors as a quantum superposition using qubit states and bipolar Progressive Matrix, a visual reasoning task over the symbolic attributes vector representation. This yields a quadratic speedup over classical of the objects, and significantly outperforms state-of-the-art search methods and effectively mitigates Hypervector Factorization pure DNN and neuro-symbolic AI solutions in both accuracy and capacity issues.