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.

本文提出了一种量子算法，用于有效地解码超向量，这是从超向量中提取原子元素的关键过程，是可解释学习和信息检索中超维计算（HDC）模型的重要任务。我们通过利用 HDC 和量子计算之间的相似之处，并利用量子算法的加速能力，提出了 HDQF，一种创新的量子计算方法，以解决超维素分解容量问题，实现了二次加速。