Hyperdimensional Quantum Factorization

TL;DR

This paper introduces HDQF, a quantum algorithm that significantly accelerates hypervector factorization in Hyperdimensional Computing, enabling more efficient decoding of complex data representations.

Contribution

The paper presents a novel quantum algorithm, HDQF, that offers quadratic speedup for hypervector factorization, addressing a key computational bottleneck in HDC models.

Findings

HDQF achieves quadratic speedup over classical methods.

HDQF effectively mitigates hypervector factorization capacity issues.

Quantum encoding of factors enhances decoding efficiency.

Abstract

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.