My weekend read. A very interesting paper on the new computing paradigm: Hyper-Dimensional Computing (HDC) and how to implement it on a quantum computer (QHDC). This is basically a specialized form of vector embeddings used in all LLMs, but here with some very specific operations. Embedding vectors of words are not trained like in LLMs, but initialized randomly, while more complex concepts built upon these words are developed with the specialized and very simple algebric operations : binding, bundling, permutation and similarity search. Mathematically, this is a complete set for various cognitive tasks like analogy making and classifications. HDC was developed as brain-inspired model, where the brain represents concepts using large number of neurons (hyper-dimensional vectors).
The authors from Cleveland Clinic have implemented it nicely on the quantum computer (Heron r3), but at a very small scale. Vectors are represented by quantum state phases, Binding is implemented with phase operations, Bundling with a unitary block operation LCU+OAA, Permutation with QFT and (cosine) Similarity calcualtion with Hadamard test.
Of course, this is far away from quantum utility now. It requires very deep circuits for LCU operation. But it shows a very nice fit of the four algebraic operations to quantum operations, and is a very interesting example of the quantum-native symbolic AI.
Sasha Lazarevic, October 2026