发表机构
University of California, Irvine（加利福尼亚大学欧文分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对超维计算中高成本的超向量分解问题，提出量子比特高效框架，引入对数超向量和绑定编码及可逆查找算子，结合改进搜索过程，保持搜索复杂度同时大幅减少量子比特使用，经实验验证效果显著。
AI 中文摘要
超维计算（HDC）使用维度为\(D\)的高维超向量来表示符号。在超向量分解中，目标是从一个有界目标超向量中恢复\(F\)个组成超向量，每个超向量都从大小为\(N\)的码本中抽取。这需要在\(N^F\)个候选元组中进行搜索，使得该任务在大规模时计算成本过高。最近的量子方法提供了二次搜索优势，但通常依赖于量子比特低效的\(O(D)\)量子比特超向量表示。我们提出了一种用于HDC分解的量子比特高效量子框架，将表示成本降低到\(O(\log D)\)。该框架引入了对数超向量和绑定编码，以及用于密集超向量电路级操作的可逆超向量查找算子。结合改进的Dürr-Høyer搜索过程，该方法在保持\(O(\sqrt{N^F})\)搜索复杂度的同时，大幅减少了量子比特的使用。实验结果验证了正确的相似性计算、在可执行范围内的准确分解，以及与基于显式\(D\)量子比特超向量编码的基线相比显著改进的量子比特缩放，实现了多达\(2000\)倍的量子比特减少。
英文摘要
Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension $D$. In hypervector decomposition, the objective is to recover $F$ constituent hypervectors, each drawn from a codebook of size $N$, from a bound target hypervector. This requires searching over $N^F$ candidate tuples, making the task computationally prohibitive at scale. Recent quantum approach provides a quadratic search advantage, but typically rely on qubit-inefficient $O(D)$-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to $O(\log D)$. The framework introduces logarithmic hypervector and binding encodings, together with a reversible hypervector lookup operator for circuit-level manipulation of dense hypervectors. Combined with a modified Dürr-Høyer search procedure, the method preserves $O(\sqrt{N^F})$ search complexity while substantially reducing qubit usage. Experimental results validate correct similarity computation, accurate decomposition in executable regimes, and significantly improved qubit scaling over baselines based on explicit $D$-qubit hypervector encodings, achieving up to $2{,}000\times$ fewer qubits.
CommentsAccepted to ICCAD 2026
