# Hyperdimensional Quantum Factorization

arXiv: https://arxiv.org/abs/2406.11889 · HTML: https://mlsanity.com/paper/2406.11889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [A theory of sequence indexing and working memory in recurrent neural networks](https://mlsanity.com/paper/1803.00412/) (2018)
- [GraphHD: Efficient graph classification using hyperdimensional computing](https://mlsanity.com/paper/2205.07826/) (2022)
- [Self-Attention Based Semantic Decomposition in Vector Symbolic Architectures](https://mlsanity.com/paper/2403.13218/) (2024)

## Abstract (arXiv)

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.